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A FRAGMENT.

LONDON :
K. CLAY, PRINTER, BREAD-STREET-HILL.

THE NINTH

BRIDGEWATER TREATISE

A FRAGMENT.

CHARLES B ABB AGE, ESQ

"We may thus, with the greatest propriety, deny to the mechanical philosophers
and mathematicians of recent times any authority with regard to their views of
the administration of the universe ; we have no reason whatever to expect from
their speculations any help, when we ascend to the first cause and supreme ruler
of the universe. But we might perhaps go farther, and assert that they are in
some respects less likely than men employed in other pursuits, to make any clear
advance towards sucli a subject of speculation." — Bridgewatcr Treatise, by the
Rev. Wm. Whewell, p. 334.

LONDON:
JOHN MURRAY, ALBEMARLE STREET.

MDCCC XXXVII.

CONTENTS.

Page
Preface v

Chapter I.
Nature of the Argument 23

Chapter II.

Argument in favour of Design from the changing of

Laws in Natural Events 30

Chapter III.

Argument to show that the Doctrines in the preced-
ing Chapter do not lead to Fatalism .... 50

Chapter IV.

On the Account of the Creation, in the First Chapter

of Genesis 63

11 CONTENTS.

Chapter V.

Page

Further View of the same Subject 72

Chapter VI.
Of the Desire of Immortality 82

Chapter VII.
On Time 88

Chapter VIII.

Argument from Laws intermitting— on the Nature of

Miracles 93

Chapter IX.

On the permanent Impression of our Words and

Actions on the Globe we inhabit 109

Chapter X.
On Hume's Argument against Miracles . . . . 118

Chapter XI.

A priori Argument in favour of the Occurrence of

Miracles 133

Chapter XII.
Thoughts on the Nature of Future Punishments . 143

CONTEiNTS. i4^

Chapter XIII.

Page

Reflections on Free Will 151

Chapter XIV.
Thoughts on the Origin of Evil 156

Conclusion 157

APPENDIX.

Note A. On the great Law which regulates Matter . 163

B. On the Calculating Engine 170

C. Extract from the Theory of Probabilities

of La Place 173

D. Note to Chap. VIII. on Miracles ... 175

E. Note to Chap. X. on Hume's Argument

against Miracles . 176

F. On the Consequences of Central Heat . . 182

G. On the Action of Existing Causes in pro-

ducing Elevations and Subsidences in
Portions of the Earth's Surface . . . 187

H. Tables showing the Expansion of Beds of

Granite variously heated 198

I. Extracts from Letters of Sir John Herschel 202
B 2

IV CONTENTS.

Page
K. On the Elevation of Beaches by Tides . . 218

L. On Ripple Mark 222

M. On the Age of Strata, as inferred from the

Rings of Trees embedded in them . . 226

N. On a Method of multiplying Illustrations

from Wood-Cuts 235

PREFACE.

The volume here presented to the public does
not form a part of that series of works com-
posed at the desire of the trustees who directed
the application of the bequest of £8000, by
the late Earl of Bridgewater, for the purpose
of advancing arguments in favour of Natural
Rehgion.

VI PREFACE.

I have, however, thought, that in furthering
the intentions of the testator, by pubHshing
some reflections on that subject, I might be
permitted to connect with them a title which
has now become famiharly associated, in the
pubHc mind, with the evidences in favour of
Natural Religion.

The Bridgewater Treatises were restricted by
the founder to the subject of Natural Rehgion ;
and I had intended not to have deviated from
their example. In the single instance in which
the question of miracles has been discussed, I
was led so irresistibly, by the very nature of the
illustrations employed in the former argument,
to the view there proposed, that I trust to
being excused for having ventured one step
beyond the strict limits of that argument, by
entering on the first connecting link between
natural religion and revelation.

The same argument will produce very various

PREFACE. Vll

degrees of conviction on different minds ;
and much of this difference will depend on
the extent of previous information, and on
the strength of the reasoning faculty in those
to whom the argument is addressed. To the
great variety, therefore, of the illustrations
which have been adduced in proof of design
and of benevolence in the works of the
Creator, there can be no objection. In truth,
to the cultivated eye of science, the origin and
consequences of the mightiest hurricane, as
well as those of the smallest leaf it scatters
in its course, equally lead to the inference
of a designing power, the more irresistibly
the more extensive the knowledge which is
brought to bear on those phenomena.

One of the chief defects of the Treatises
above referred to appears to me to arise from
their not pursuing the argument to a suffi-
cient extent. When a multitude of appa-
rently unconnected facts is traced up to some

Vlll PREFACE.

common principle, we feel spontaneously an
admiration for him who has explained to us
the connexion; and if, advancing another
stage in the investigation, he prove that other
facts, apparently at variance with that prin-
ciple, are not merely no exceptions, but are
themselves inevitable consequences of its ap-
plication, our admiration of the principle,
and our respect for its discoverer, are still
further enhanced.

But if this respect and admiration are
yielded to the mere interpreter of Nature's
laws, how much more exalted must those
sentiments become when applied to the Being
who called such principles into living exist-
ence by creating matter subservient to their
dominion — whose mind, intimately cognizant
of the remotest consequences of the present
as well as of all other laws, decreed existence
to that one alone, which should comprehend
within its grasp the completion of its destiny —

PKEl'ACE. IX

which should require no future intervention
to meet events unanticipated by its author, in
whose omniscient mind we can conceive no
infirmity of purpose — no change of intention !

The object of these pages, as of the Bridge-
water Treatises, is to show that the power and
knowledge of the great Creator of matter and
of mind are unlimited. Deeply engaged in
those other pursuits from which my chief argu-
ments are drawn, I regret the impossibility of
bestowing on their full development that time
and attention which the difficulty and import-
ance of the subject equally deserve ; and in
committing these fragments to the press,
perhaps in too condensed a form, I wish them
to be considered merely as suggestions in-
tended to direct the reader's attention to lines
of argument which appear to me new, and to
views of nature which appear more magnifi-
cent, than those with which I was previously
acquainted.

X PREFACE.

Probably I should not have been induced
to place my reflections on the subject before
the public, had I not, in common with other
cultivators of the more abstract branches of
mathematical science, felt that a prejudice,
which I had believed to have been long eradi-
cated from every cultivated mind, had lately
received support, at least to a certain extent,
from a chapter in the first* of the Bridgewater
Treatises ; and in a still greater degree, from
a work of a far different order — -one, however,
which derived its only claim to notice from the
circumstance of its appearing under the sanc-
tion of the University of Oxford.

The prejudice to which I allude is, that the
pursuits of science are unfavourable to religion.

There are two classes of men most deeply
impressed with the conviction of the very

* It was the first in the order of puhlication.

PREFACE. XI

limited extent of human knowledge — those
whose contracted information renders them
eminent examples of the fact, and those whose
wide grasp of many of its profoundest branches
has taught them, by lengthened experience, that
each accession to their stock but enables them
to view a larger portion of its illimitable field.
Those who belong to the first of these classes
must acquire the alphabet of science, in order
to understand knowledge, and the elements
of modesty, to use it with dignity. When
they have thus graduated in the " infant
school" of philosophy, they may perhaps
understand the argument, and perchance be
w^orthy of a reply, — but not till then.

In that chapter of the first Bridgewater
Treatise to which I have referred, the charge
seems not even to be limited to those who
pursue that branch of science which is con-
versant with the properties of pure number,
and with abstractions of a like nature, but

XII PREFACE.

applies to all who cultivate deductive processes
of reasoning.

It is maintained by the author, that long
application to such inquiries disqualifies the
mind from duly appreciating the force of that
kind of evidence which alone can be adduced
in favour of Natural Theology.

*' We may thus, with the greatest propriety, deny to the
mechanical philosophers and mathematicians of recent times
any authority with regard to their views of the administra-
tion of the universe ; we have no reason whatever to expect
from their speculations any help, when we ascend to the
first cause and supreme ruler of the universe. But we
might perhaps go farther, and assert that they are in some
respects less likely than men employed in other pursuits,
to make any clear advance towards such a subject of specu-
lation."— Bridgewater Treatise, hy the'REV. Wm. Whewell,
p. 334.

Admitting, for the sake of argument, that
there have been individuals, possessed of high
intellectual powers, successfully devoted to
those subjects, who have arrived by reasoning
at conclusions respecting the First Cause,

PREFACE. Xlll

totally opposite to those entertained by Mr.
Whevvell and myself, I should still be very
reluctant to endeavour to invalidate the in-
fluence of their conclusions, by any inquiry
either into their intellectual or their moral
character. Reasoning is to be combated and
refuted by reasoning alone. Any endeavour to
raise a prejudice, or throw the shadow of an
imputation, either implies the existence of
some latent misgiving in the minds of those
who employ such weapons, or is a tacit admis-
sion that the question is beyond the grasp of
one at least of the debaters.

Who that has studied their works ever
dreamed of inquiring into the moral or intel-
lectual character of Euclid or Archimedes, for
the purpose of confirming or invalidating his
belief in their conclusions ? Who that pos-
sesses confidence in his own reason, justified
by a laborious cultivation and successful
exercise of that faculty, fails to anatomize and

XIV PREFACE.

refute the arguments, rather than analyze the
mental or moral habits of those from whom he
differs ?

The only case in which such extraneous
matters can be fairly called in, is when facts
are stated resting on testimony. Then it is
not only just, but it is necessary for the
sake of truth, to inquire into the habits of
mind of him by whom they are adduced ; —
whether he possesses sufficient talent and
precision to enable him to state precisely
what his senses convey to him, and nothing
more ; or, if he receive information from
others, whether he is credulous or cautious.
In both cases, it is necessary to inquire into
moral feelings, in order to be assured that
there is no wilful mis-statement in the
groundwork of his reasoning. And even
when this is well established, it is still ne-
cessary to inquire whether he had any
personal, professional, or pecuniary interest

PREFACE. XV

which may insensibly have influenced his
mind in one direction.

Such I conceive to be the sound distinction
between those branches of knowledge resting
on facts open to the observation of all, sup-
ported by reasoning addressed to the under-
standings of all, — and those other branches
in which reasoning is mixed up with testi-
mony. In the former, the argument is every
thing — the character nothing: in the latter,
the character must be sifted as well as the
arguments.

Feeling convinced that the truths of Natural
Religion rest on foundations far stronger than
those of any human testimony ; that they are
impressed in indelible characters, by almighty
power, on every fragment of the material
world, I cannot but regret that reflections
should have been made, in connexion with
this subject, calculated to throw the least

XVI PREFACE.

shadow of doubt on evidence otherwise irre-
sistible.

As, however, these views of the nature of
the question may not bring that conviction
to other minds, which they do to my own,
and as one of the disturbing forces which act
on our minds has been strongly put forward,
it is but justice to state the whole of them.
It requires but little insight into man's
heart to perceive that profession and pro-
fessional advancement — that power and
wealth — have a far more frequent and more
effective influence on his judgment than any
mental habits he may be supposed to have
cultivated.

It may be right then to state, that the
author of these pages has always been an ardent
but not an exclusive cultivator of some of
the more abstract branches of mathematical
science. In pursuing one of those inquiries,

PREFACK. XVll

amongst the most recondite and apparently
the most removed from any practical applica-
tion, he was struck with the bearing of some
of the results which presented themselves, on
the question of Natural Religion ; and these
he has endeavoured to place before the reader,
in the following pages.

The author belongs to no profession in
which he can hope for advancement, if he suc-
cessfully advocate one side of the question, oi
in which his prospects can be injured by can-
didly stating any arguments on the other.
He has not been invited by men high in the
State, and deservedly respected, to support
that great basis which precedes all revelation,
and on which it must all rest. Nor has any
sum of money been assigned to him, that,
whatever the mercantile success or failure
of the present volume may be, he shall,
on its publication, reap a large pecuniary
reward.

XVlll PREFACE.

Having chosen a career to which the insti-
tutions of the country hold out none of those
great prizes that stimulate professional exer-
tions, and which constrain men to yield a cer-
tain degree of deference to the opinions, sound
or unsound, of their countrymen, he has, on
the one hand, nothing to hope from their ap-
probation, and, on the other, is equally exempt
from any fear of their censure ; and, had his
conviction been as strongly opposed to the
doctrines this Fragment advocates, as it is in
their favour, he would, had a fit occasion
presented itself, fearlessly have laid before the
world the arguments which had forced his
mind to that conviction.

In conclusion, I have to express to my fel-
low-labourers in the cause, my hope that they
will put no unkind interpretation on these re-
marks, which, founded on principles of human
nature, are necessarily of general application ;
that they will see that motives alien, in my

piii:rAcr:. xix

own opinion, to the subject, having been once
introduced, candour to those who differ from
us, as well as a deference to truth itself, com-
pelled me to state them fully.

CHARLES BABBAGE.

Dorset-street,
Manchester-square,

Jpril 1837,

XXI

The following account of the origin of the Bridge-
water Treatises, is extrcictcd from one of these
works : —

" The Right Honourable and Reverend Francis Henry, Earl of
Bridgewater, died in the month of February, 1829; and, by his
last will and testament, bearing date the 25th of February, 1825,
he directed certain Trustees therein named, to invest in the public
funds the sum of eight thousand pounds sterling; this sum, with
the accruing dividends thereon, to be held at the disposal of
the President, for the time being, of the Royal Society of London,
to be paid to the person or persons nominated by him. The tes-
tator further directed, that the person or persons selected by the
said President should be appointed to write, print, and publish,
one thousand copies of a work " On the Power, Wisdom, and
Goodness of God, as manifested in the Creation ;" illustrating such
work by all reasonable arguments, as, for instance, the variety
and formation of God's creatures in the animal, vegetable, and
mineral kingdoms; the effect of digestion, and thereby of conver-
sion; the construction of the hand of man, and an infinite variety
of other arguments: as also by discoveries, ancient and modern,
in arts, sciences, and the whole extent of literature. He desired,
moreover, that the profits arising from the sale of the works
so published should be paid to the authors of the works.

The late President of the Royal Society, Davies Gilbert, Esq.,
requested the assistance of his Grace the Archbishop of Canterbury,
and of the Bishop of London, in determining upon the best mode
of carrying into effect the intentions of the testator. Acting with
their advice, and with the concurrence of a nobleman immediately
connected with the deceased, Mr. Davies Gilbert appointed eight
gentlemen to write separate Treatises on the different branches of
the subject."

XXll

Of the eight gentlemen so appointed, four were of
the clerical, and four of the medical, profession.
Their names, and the subjects assigned to them, are
as follows: —

1. The Rev. Thomas Chalmers, D.D., Professor of Divinity in

the University of Edinburgh — " On the Adaptation of Ex-
ternal Nature to the Moral and Intellectual Constitution
of Man."

2. The Rev. Wm. Buckland, D.D., F.R.S., Canon of Christ

Church, and Professor of Geology in the University of
Oxford — •' On Geology and Mineralogy."

3. The Rev. Wm. Whewell, M.A., F.R.S., Fellow of Trinity

College,Cambridge — " OnAstronomy andGeneral Physics."

4. The Rev. Wm. Kirby, M.A., F.R.S.—" On the History,

Habits, and Instincts of Animals."

5. John Kidd, M.D., F.R.S., Regius Professor of Medicine in

the University of Oxford — " On the Adaptation of Ex-
ternal Nature to the Physical Condition of Man,"

6. Sir Charles Bell, K.H., F.R.S.—*' The Hand: its Me-

chanism and Vital Endowments, as evincing Design."

7. Peter Mark Roget, M.D., Fellow of, and Secretary to, the

Royal Society — " On Animal and Vegetable Physiology."

8. Wm. Prout, M.D., F.R.S.—" On Chemistry, Meteorology,

and the Function of Digestion."

CHAP. I.

NATURE OF THE ARGUMENT.

The notions we acquire of contrivance and
design arise from comparing our observations
on the v^orks of other beings v^ith the inten-
tions of which we are conscious in our own
undertakings. We take the highest and best of
human faculties, and, exalting them in our
imagination to an unlimited extent, endeavour
to attain an imperfect conception of that
Infinite Power which created every thing
around us. In pursuing this course, it is
evident that we are liable to impress upon the

24 INTRODUCTION.

notion of Deity thus shadowed out, many
traces of those imperfections in our own
limited faculties which are best known to
those who have most deeply cultivated them.
It is also evident that all those discoveries
which arm human reason with new power, and
all additions to our acquaintance with the
material world, must from time to time render
a revision of that notion necessary. The
present seems to be a fit occasion for such a
revision.

Many excellent and rehgious persons not
deeply versed in what they mistakenly call
" human knowledge,'' but which is in truth the
interpretation of those laws that God himself
has impressed on his creation, have endea-
voured to discover proofs of design in a
multitude of apparent adaptations of means
to ends, and have represented the Deity as
perpetually interfering, to alter for a time the
laws he had previously ordained; thus by
implication denying to him the possession

INTRODUCTION. 25

of that foresight which is the highest attribute
of omnipotence. Minds of this order, insen-
sible of the existence of that combining and
generahsing faculty which gives to human
intellect its greatest development, and tied
down by the trammels of their own peculiar
pursuits, have in their mistaken zeal not per-
ceived their own unfitness for the mighty task,
and have ventured to represent the Creator
of the universe as fettered by the same
infirmities as those by which their own limited
faculties are subjugated. To causes of this
kind must in some measure be attributed an
opinion which has been industriously spread,
that minds highly imbued with mathematical
knowledge are disqualified, by the possession
of that knowledge, and by the habits of mind
produced during its acquisition, from rightly
appreciating the works of the Creator.

At periods and in countries in which the
knowledge of the priests exceeded that of the
people, science has always been held up by the

26 INTRODUCTION.

former class as an object of regard, and its
crafty possessors have too frequently defiled its
purity by employing their knowledge for the
delusion of the people. On the other hand,
at times and in countries in which the know-
ledge of the people has advanced beyond
that of the priesthood, the ministers of the
temple have too often been afraid of the
advance of knowledge, and have threatened
with the displeasure of the Almighty those
engaged in employing the faculties he has
bestowed on the study of the works he has
created. At the present period, when know-
ledge is so universally spread that neither
class is far in advance of the other, — when
every subject is submitted to unbounded
discussion, — when it is at length fully acknow-
ledged that truth alone can stand unshaken by
perennial attacks, and that error, though for
centuries triumphant, must fall at last, and
leave behind no ashes from which it may
revive, the authority of names has but little
weight : facts and arguments are the basis of

INTRODUCTION. 27

creeds, and convictions so arrived at are the
more deeply seated, and the more enduring,
because they are not the wild fancies of pas-
sion or of impulse, but the deliberate results
of reason and reflection.

It is a condition of our race that we must
ever w^ade through error in our advance
towards truth ; and it may even be said that
in many cases we exhaust almost every variety
of error before we attain the desired goal.
But truths, once reached by such a course,
are always most highly valued ; and when, in
addition to this, they have been exposed to
every variety of attack which splendid talents
quickened into energy by the keen perception
of personal interests can suggest, — when they
have revived undying from unmerited neglect ;
when the anathema of spiritual, and the arm
of secular power have been found as im.potent
in suppressing, as their arguments were in
refuting them, then they are indeed irre-
sistible. Thus tried and thus triumphant in

28 INTRODUCTION.

the fiercest warfare of intellectual strife, even
the temporary interests and furious passions
which urged on the contest, have contributed
in no small measure to establish their value,
and thus to render these truths the permanent
heritage of our race.

Viewed in this light, the propagation of an
error, although it may be unfavourable or
fatal to the temporary interest of an individual,
can never be long injurious to the cause of
truth. It may, at a particular time, retard its
progress for a while, but it repays the trans-
itory injury by a benefit as permanent as the
duration of the truth to which it was opposed.
This reasoning is offered for the purpose of
proving that the toleration of the fullest dis-
cussion is most advantageous to truth. It is
not offered as the advocate of or the apology
for error ; and whilst it is admitted that every
person who wilfully puts forward as valid an
argument the soundness of which he doubts,
incurs a deep responsibility, it is also some

INTRODUCTION. 29

satisfaction to reflect that the delay thus occa-
sioned to the great cause can be but small,
and that those who in sincerity of heart main-
tain arguments which a more advanced state
of knowledge shall prove to be erroneous, may
yet ultimately contribute, by that very publi-
cation, to its speedier establishment.

CHAP. II.

ARGUMENT IN FAVOUR OF DESIGN FROM THE
CHANGING OF LAWS IN NATURAL EVENTS.

The estimate we form of the intellectual
capacity of our race, is founded on an exa-
mination of those productions which have
resulted from the loftiest flights of individual
genius, or from the accumulated labours of
generations of men, by whose long-continued
exertions a body of science has been raised
up, surpassing in its extent the creative powers
of any individual, and demanding for its deve-
lopment a length of time, to which no single
life extends.

ARGUMENT IN FAVOUR OF DESIGN. 31

The estimate we form of the Creator of the
visible world rests ultimately on the same
foundation. Conscious that we each of us em-
ploy, in our own productions, means intended
to accomplish the objects at which we aim, and
tracing throughout the actions and inventions
of our fellow-creatures the same intention, —
judging also, of their capacity by the fit selec-
tion they make of the means by which they
work, we are irresistibly led, when we con-
template the natural world, to attempt to
trace each existing fact presented to our senses
to some precontrived arrangement, itself per-
haps the consequence of a yet more general
law; and where the most powerful aids by
which we can assist our limited faculties fail in
enabling us to detect such connexions, we still,
and not the less, believe that a more extended
inquiry, or higher powers, would enable us to
discover them.

The larger the number of consequences
resulting from any law, and the more they are
foreseen, the greater the knowledge and intel-

ARGUMENT IN

ligence we ascribe to the being by which it
was ordained. In the earher stages of our
knowledge, we behold a multitude of distinct
laws, all harmonizing to produce results which
we deem beneficial to our own species : as
science advances, many of these minor laws
merge into some more general principles ; and
with its higher progress these secondary prin-
ciples appear, in their turn, the mere conse-
quences of some still more general law. Such
has been the case in two of the most curious
and most elaborately cultivated branches of
human knowledge, the sciences of astronomy
and optics* All analogy leads us to infer, and
new discoveries continually direct our expecta-
tion to the idea, that the most extensive laws
to which we have hitherto attained, converge to
some few simple and general principles, by
which the whole of the material universe is
sustained, and from which its infinitely varied
phenomena emerge as the necessary conse-

quences

See Note A in the Appendix.

FAVOUR OF DKSIGN. 33

To illustrate the distinction between a sys-
tem to which the restoring hand of its con-
triver is applied, either frequently or at distant
intervals, and one which had received at its
first formation the impress of the will of its
author, foreseeing the varied but yet neces-
sary laws of its action, throughout the whole
extent of its existence, we must have recourse
to some machine, the produce of human skill.
But for as all such engines must ever be
placed at an immeasurable interval below
the simplest of Nature's works, yet, from the
vastness of those cycles which even human
contrivance in some cases unfolds to our view,
we may perhaps be enabled to form a faint
estimate of the magnitude of that lowest step
in the chain of reasoning, which leads us up
to Nature's God.

The illustration which I shall here employ
will be derived from the results afforded by
the Calculating Engine ;* and this I am the

* The reader will find a short account of this engine in
the Appendix, Note B.

ARGUMENT IN

more disposed to use, because my own views
respecting the extent of the laws of Nature
were greatly enlarged by considering it, and
also because it incidentally presents matter
for reflection on the subject of inductive
reasoning. Nor will any difficulty arise from
the complexity of that engine ; no knowledge
of its mechanism, nor any acquaintance with
mathematical science, being necessary for
comprehending the illustration, it being suffi-
cient merely to conceive that computations of
great complexity can be effected by me-
chanical means.

Let the reader imagine that such an engine
has been adjusted; and that it is moved by a
weight ; and that he sits dow^n before it, and
observes a wheel, which revolves through a
small angle round its axis, at short intervals,
presenting to his eye, successively, a series
of numbers engraved on its divided circum-
ference.

FAVOUR OF DESIGN. 35

Let the figures thus seen he the scries 1, 2,
3, 4, 5, &c., of natural numhers, each of which
exceeds its immediate antecedent by unity.

Now, reader, let me ask how long you will
have counted before you are firmly convinced
that the engine has been so adjusted that it
will continue whilst its motion is maintained,
to produce the same series of natural numbers ?
Some minds are so constituted, that after
passing the first hundred terms, they will be
satisfied that they are acquainted with the
law. After seeing five hundred terms, few^ will
doubt ; and after the fifty-thousandth term
the propensity to believe that the succeeding
term will be fifty thousand and one, will be
almost irresistible. That term zalll be fifty
thousand and one ; and the same regular suc-
cession will continue ; the five-millionth and
the fifty-millionth term will still appear in
their expected order ; and one unbroken chain
of natural numbers will pass before your eyes,
from one up to one hundi^ed million.

36 ARGUMENT IN

True to the vast induction which has been
made, the next succeeding term will be one
hundred miUion and one ; but the next num-
ber presented by the rim of the wheel, in-
stead of being one hundred milUon and two,
is one hundred million ten thousand and two.
The whole series from the commencement

being thus : —

1
2

3
4

• • •

99,999,999

100,000,000

regularly as far as 100,000,001

100,010,002 the law changes

100,030,003

100,060,004

100,100,005

100,150,006

100,210,007

100,280,008

FAVOUR OF DESIGN. 37

The law which seemed at first to govern this
series fails at the hundred million and second
term. This term is larger than we expected,
by 10,000. The next term is larger than was
anticipated, by 30,000, and the excess of each
term above what we had expected forms the

following table : —

10,000

30,000

60,000
100,000
150,000

being, in fact, the series of triangular num-
hers,^ each multiplied by 10,000.

* The numbers 1, 3, 6, 10, 15, 21, 28, &c. are formed
by adding the successive terms of the series of natural
numbers thus ;

1 = 1.
1+2 = 3.
1+2 + 3 = 6.
1 + 2 + 3 + 4 = 10, &c.
They are called triangular numbers, because a number
of points corresponding to any term can always be placed
in the form of a triangle, for instance : —

Ob ARGUMENT IN

If we now continue to observe the num-
bers presented by the wheel, we shall find,
that for a hundred, or even for a thousand
terms, they continue to follow the new law
relating to the triangular numbers ; but after
watching them for 2761 terms, we find that
this law fails in the case of the 2762d term.

If we continue to observe, we shall discover
another law then coming into action, which
also is dependent, but in a different manner,
on triangular numbers. This will continue
through about 1430 terms, when a new law is
again introduced, which extends over about
950 terms ; and this too, like all its prede-
cessors, fails, and gives place to other laws,
which appear at different intervals.

Now it must be remarked, that the law
that each number presented by the Engine is
greater by unity than the preceding number,
which law the observer had deduced from an
induction of a hundred million instances, was

FAVOUR OF DESIGN. 39

not the true law that regulated its action ; and
that the occurrence of the number 100,010,002
at the 1 00,000,002d term, was as necessari/ a
consequence of the original adjustment, and
might have been as fully foreknown at the
commencement, as was the regular succession
of any one of the intermediate numbers to
its immediate antecedent. The same remark
applies to the next apparent deviation from
the new law, which was founded on an in-
duction of 2761 terms, and also to the suc-
ceeding law ; with this limitation only — that
whilst their consecutive introduction at various
definite intervals is a necessary consequence
of the mechanical structure of the engine, our
knowledge of analysis does not enable us to
predict the periods themselves at which the
more distant laws will be introduced.

Such are the facts which, by a certain ad-
justment of the Calculating Engine, would be
presented to the observer. Now, let him ima-
gine another engine, offering to him precisely

40 ARGUMENT IN

the same figures in the same order of suc-
cession ; but let it be necessary for the maker
of that other engine, previously to each appa-
rent change in the law, to make some new
adjustment in the structure of the engine itself,
in order to accomplish the ends proposed.
The first engine must be susceptible of having
embodied in its mechanical structure, that
more general law of which all the observed
laws were but isolated portions, — a law so
complicated, that analysis itself, in its present
state, can scarcely grasp the whole question.
The second engine might be of far simpler
contrivance ; it must be capable of receiving
the laws impressed upon it from without, but
is incapable, by its own intrinsic structure, of
changing, at definite periods, and in unhmited
succession, those laws by which it acts.
Which of these two engines would, in the
reader's opinion, give the higher proof of skill
in the contriver? He cannot for a moment
hesitate in pronouncing that that on which,
after its original adjustment, no superintend-

FAVOUR OF DESICJN. 41

ance was required, displayed far greater in-
genuity than that which demanded, at every
change in its law, the intervention of its
contriver.

The engine we have been considering is but
a very small portion (about fifteen figures)
of a much larger one, which was preparing,
and partly executed ; it was intended, when
completed, that it should have presented at
once to the eye about one hundred and thirty
figures. In that more extended form which
recent simplifications have enabled me to give
to machinery constructed for the purpose of
making calculations, it will be possible, by cer-
tain adjustments, to set the engine so that it
shall produce the series of natural numbers in
regular order, from unity up to a number ex-
pressed by more than a thousand places of
figures. At the end of that term, another and a
different law shall regulate the succeeding
terms ; this law shall continue in operation per-
haps for a number of terms, expressed by unity^

42 ARGUMEiNT IN

followed by a thousand zeros, or 10^^"^; at
which period another law shall be introduced,
and, like its predecessors, govern the figures
produced by the engine during a third of those
enormous periods. This change of laws might
continue without limit ; each individual law
destined to govern for millions of ages the cal-
culations of the engine, and then give way to
its successor to pursue a like career.*

Thus a series of laws, each simple in itself,
successively spring into existence, at distances
almost too great for human conception. The
full expression of that wider law, which com-
prehends within it this unlimited sequence of
minor consequences, may indeed be beyond
the utmost reach of mathematical analysis :
but of one remarkable fact, however, we are

* It has been supposed that ten turns of the handle of the
calculating engine might be made in a minute, or about five
hundred and twenty-six millions in a century. As in
this case, each turn would make a calculation, after the lapse
of a million of centuries, only the fifteenth place of figures
would have been reached.

FAVOUR OF DESIGN. 43

certain — that the mechanism brought into
action for the purpose of changing the nature
of the calculation from the production of its
more elementary operations into those highly
complicated ones of which we speak, is itself
of the simplest kind.

In contemplating the operations of laws so
uniform during such immense periods, and
then changing so completely their apparent
nature, whilst the alterations are in fact only
the necessary consequences of some far higher
law, we can scarcely avoid remarking the
analogy which they bear to several of the
phenomena of nature.

The laws of animal life which regulate the
caterpillar, seem totally distinct from those
which, in the subsequent stage of its existence,
govern the butterfly. The difference is still
more remarkable in the transformations un-
dergone by that class of animals which spend
the first portion of their life beneath the sur-
face of the waters, and the latter part as

44 ARGUMENT IN

inhabitants of air. It is true that the periods
during which these laws exist are not, to our
senses, enormous, hke the mechanical ones
above mentioned ; but it cannot be doubted
that, immeasurably more complex as they are,
they were equally foreknown by their Author :
and that the first creation of the egg of the
moth, or the libellula, involved within its
contrivance, as a necessary consequence, the
Avhole of the subsequent transformations of
every individual of their respective races.

In turning our views from these simple con-
sequences of the juxtaposition of a few wheels,
it is impossible not to perceive the parallel
reasoning, as applied to the mighty and far
more complex phenomena of nature. To call
into existence all the variety of vegetable
forms, as they become fitted to exist, by the
successive adaptations of their parent earth, is
undoubtedly a high exertion of creative power.
When a rich vegetation has covered the globe,
to create animals adapted to that clothing.

FAVOUR OF DESIGN. 45

which, deriving nourishment from its luxuri-
ance, shall gladden the face of nature, is not
only a high but a benevolent exertion of
creative power. To change, from time to time,
after lengthened periods, the races which exist,
as altered physical circumstances may render
their abode more or less congenial to their
habits, by allowing the natural extinction of
some races, and by a new creation of others
more fitted to supply the place previously
abandoned, is still but the exercise of the same
benevolent power. To cause an alteration in
those physical circumstances — to add to the
comforts of the newly created animals — all
these acts imply power of the same order, a
perpetual and benevolent superintendence, to
take advantage of altered circumstances, for the
purpose of producing additional happiness.

But, to have foreseeuy at the creation of
matter and of mind, that a period would ar-
rive when matter, assuming its prearranged
combinations, would become susceptible of

ARGUMENT IN

the support of vegetable forms; that these
should in due time themselves supply
the pabulum of animal existence ; that suc-
cessive races of giant forms or of micro-
scopic beings should at appointed periods
necessarily rise into existence, and as inevi-
tably yield to decay ; and that decay and
death — the lot of each individual existence
— should also act with equal power on the
races which they constitute ; that the extinc-
tion of every race should be as certain as the
death of each individual ; and the advent of
new genera be as inevitable as the destruc-
tion of their predecessors ; — to have foreseen
all these changes, and to have provided, by
one comprehensive law, for all that should
ever occur, either to the races themselves, to
the individuals of which they are composed,
or to the globe which they inhabit, manifests
a degree of power and of knowledge of a far
higher order.

The vast cycles in the geological changes

FAVOUR OF DESIGN. 47

that have taken place in the earth's surface,
of which we have ample evidence, offer
another analogy in nature to those mechanical
changes of law from which we have endea-
voured to extract a unit sufficiently large to
serve as an imperfect measure for some of
the simplest works of the Creator.

The gradual advance of Geology, during the
last twenty years, to the dignity of a science,
has arisen from the laborious and extensive
collection of facts, and from the enlightened
spirit in which the inductions founded on those
facts have been deduced and discussed. To
those who are unacquainted with this science,
or indeed to any person not deeply versed in
the history of this and kindred subjects, it is
impossible to convey a just impression of the
nature of that evidence by which a multitude
of its conclusions are supported : — evidence
in many cases so irresistible, that the records
of the past ages, to which it refers, are traced
in language more imperishable than that of

4 8 ARGUMENT IN

the historian of any human transactions ; the
rehcs of those beings, entombed in the strata
which myriads of centuries have heaped upon
their graves, giving a present evidence of their
past existence, with which no human testi-
mony can compete. It is found that each
additional step, in the grouping together of
the facts of geology, confirms the view that
the changes of our planet, since it has been
the abode of man, is but as a page in the
massive volumes of its history, every leaf of
which, written in the same character, conveys
to the decypherer the idea of a succession
of the same causes acting with varying inten-
sity, through unequal but enormous periods,
each period apparently distinguished by the
coming in or going out of new subsidiary laws,
yet all submitted to some still higher con-
dition, which has stamped the mark of unity
on the series, and points to the conclusion
that the minutest changes, as well as those
transitions apparently the most abrupt, have
throughout all time been the necessary, the

FAVOUR OF DESIGN. 49

inevitable consequences of some more com-
prehensive law impressed on matter at the
dawn of its existence.

50 ARGUMENT

CHAP. III.

ARGUMENT TO SHOW THAT THE DOCTRINES IN
THE PRECEDING CHAPTER DO NOT LEAD TO
FATALISM.

If all the combinations and modifications
of matter can be supposed to be traced up to
one general and comprehensive law, from
which every visible form, both in the organic
and inorganic world flows, as the necessary
consequence of the first impression of that
law upon matter, it might seem to follow that
Fate or Necessity governs all things, and that
the world around us may not be the result of
a contriving mind working for a benevolent
purpose.

AGALNST FATE. 51

Such, possibly, may be the first impression
of this view of the subject ; but it is an er-
roneous view, — one of those, perhaps, through
which it is necessary to pass, in order to arrive
at truth. Let us briefly review the labour
which the human race has expended, in at-
taining the hmited knowledge we possess. For
about six thousand years man has claimed
the earth as his heritage, and asserted his
dominion over all other beings endued with
life ; yet, during a large portion of that period,
how comparatively small has been his mental
improvement ! Until the invention of print-
ing, the mass of mankind were in many re-
spects almost the creatures of instinct. It is
true, the knowledge possessed by each gene-
ration, instead of being the gift of Nature,
was derived from the instruction of their prede-
cessors; but, how little were those lessons
improved by repeated communication ! Trans-
mitted most frequently by unenlightened in-
structors, they might lose, but could rarely
gain in value.

E 2

ARGUMENT

Before the invention of printing, acci-
dental position determined the opinions and
the knowledge of the great mass of mankind.
Oral information being almost the only kind
accessible, each man shared the opinions of
his kindred and neighbours ; and truth, which
is ever most quickly and most surely elicited
by discussion, lost all those advantages which
diversity of opinion always produces for it. The
minds of individual men, however powerful,
could address themselves only to a very small
portion of their fellow men ; their influence
was restricted by space and limited by time,
and their highest powers were not stimulated
into action by the knowledge that their reason-
ings could have effect where their voices were
unheard, or by the conviction that the truths
they arrived at, and the discoveries they
made, would extend beyond their country,
and survive their age.

But, since the invention of printing, how
different has been the position of mankind !

AGAINST FATE. 53

the nature of the instruction no longer de-
pends entirely on the knowledge of the
instructor. The village school-master com-
municates to his pupils the power of using
an instrument hy which not merely the best
of their living countrymen, but the greatest
and wisest men of all countries and all times,
may become their instructors. Even the ele-
mentary writings through which this art is
taught, give to the pupil, not the sentiments of
the teacher, but those which the public opinion
of his countrymen esteems most fit for the be-
ginner in knowledge. Thus the united opinions
of multitudes of human minds are brought
to bear even upon seemingly unimportant
points.

If such is the effect of the invention of
printing upon ordinary minds, its influence
over those more highly endowed is far greater.
To them the discussion of the conflicting opi-
nions of different countries and distant ages,
and the establishment of new truths, presents

54 ARGUMENT

a field of boundless and exalted ambition.
Advancing beyond the knowledge of their
neighbours and countrymen^ they may be ex-
posed to those prejudices which result from
opinions long stationary ; but encouraged by
the approbation of the greatest of other na-
tions, and the more enlightened of their ow^n, —
knowing that time alone is wanting to complete
the triumph of truth, they may accelerate the
approaching dawn of that day which shall
pour a flood of hght over the darkened intel-
lects of their thankless countrymen — content
themselves to exchange the hatred they expe-
rience from the honest and the dishonest into-
lerance of their contemporaries, for that higher
homage, alike independent of space and of time,
which their memory will for ever receive
from the good and the gifted of all countries
and all ages.

Until printing was very generally spread,
civilisation scarcely advanced by slow and lan-
guid steps ; since this art has become cheap.

AGAINST lATK.

its advances have been unparalleled, and its
rate of progress vastly accelerated.

It has been stated by some, that the civili-
sation of the Western World has resulted from
its being the seat of the Christian religion :
however much the mild tenor of its doctrines
is calculated to assist in producing such an
effect, that religion cannot but be injured by an
unfounded statement. It is to the easy and
cheap methods of communicating thought from
man to man, which enable a country to sift, as
it were, its whole people, and to produce, in its
science, its literature, and its arts, not the
brightest efforts of a limited class, but the
highest exertions of the most powerful minds
among a whole community ; — it is this which
has given birth to the wide-spreading civilisa-
tion of the present day, and which promises a
futurity yet more prolific. Whoever is ac-
quainted with the present state of science and
the mechanical arts, and looks back over the
inventions and civilisation which the fourteen

56 ARGUMENT

centuries subsequent to the introduction of
Christianity have produced, and compares
them with the advances made during the suc-
ceeding four centuries following the invention
of printing, will have no doubt as to the effec-
tive cause.

It is during these last three or four centu-
ries, that man, considered as a species, has
commenced the development of his intellec-
tual faculties — that he has emerged from a po-
sition in which he was almost the creature of
instinct, to a state in which every step in ad-
vance facilitates the progress of his succes-
sors. In the first period, arts were discovered
by individuals, and lost to the race ; in the
latter, the diffusion of ideas enabled the rea-
soning of one class to unite with the observa-
tions of another, and the most advanced point
of one generation became the starting post
of the next.

It is during this portion of our history that

AGAINST FATE. 57

man has become acquainted with his real posi-
tion in the universe — that he has measured the
distance from that which is to us the great
fountain of hght and heat — that he has traced
the orbits of earth's sister spheres, and calcu-
lated the paths of all their dependent worlds —
that he has arrived at the knowledge of a
law — that of gravity, which appears to go-
vern all matter, and whose remotest conse-
quences, if first traced by his telescope, are
found written in his theory ; or, if first pre-
dicted by his theory, are verified by his obser-
vations.

Simple as that law now appears, and beau-
tifully in accordance with all the observations of
past and of present times, consider what it has
cost of intellectual study. Copernicus, Galileo,
Kepler, Euler, Lagrange, Laplace, all the great
names which have exalted the character of
man, by carrying out trains of reasoning
unparalleled in every other science ; these,
and a host of others, each of whom might

ARGUMENT

have been the Newton of another field, have
all laboured to work out, the consequences
which resulted from that single law which
he discovered. All that the human mind has
produced — the brightest in genius, or the most
continuous in application, has been lavished
on the details of the law of gravity.

Had that law been other than it is — had it
been the inverse cube of the distance, for
example, it would still have required an equal
expense of genius and of perseverance to have
worked out its details. But, between the laws
represented by the inverse square, and the
inverse cube of the distance, there are inter-
posed an infinite number of other laws, each
of which might have been the basis of a
system requiring the most extensive know-
ledge to trace out its consequences. Between
every law which can be expressed by whole
numbers, whether it be direct or inverse,
an infinity of others can still be interposed.
All these might be again combined by two,

AGAINST FATE. 59

by three, or by any other combinations, and
new systems might be imagined,* submitted
to such laws. Thus, another infinity of laws,
of a far higher order — in fact, of an infinitely
higher order — might again be added to the list.
And this might still be increased by every other
combination, of which such laws admit, besides
that by addition, to which we have already
alluded, thus forming an infinity itself of so
high an order, that it is difficult to conceive.
Man has, as yet, no proof of the impossibility
of the existence of any of these laws. Each
might, for any reason we can assign, be the
basis of a creation different from our own.

It is at this point that skill and knowledge
re-enter the argument, and banish for ever the
dominion of chance. The Being who called

* Even beyond this, every law so imagined might be
interrupted by any discontinuous function ; and thus be
made to agree, for any period, with laws of simpler form,
and yet deviate, in one single, or in a certain limited num-
ber of cases, and then agree with it for ever.

60 ARGUMENT

into existence this creation, of which we are
parts, must have chosen the present form, the
present laws, in preference to the infinitely
infinite variety which he might have willed
into existence. He must have known and fore-
seen all, even the remotest consequences of
every one of those laws, to have penetrated
but a little way into one of w^hich has ex-
hausted the intellect of our whole species.

But, if such is the view we must take of the
knowledge of the Creator, when contemplating
the laws of inanimate matter — laws into whose
consequences it has cost us such accumulated
labour to penetrate — what language can w^e
speak, when we consider that the laws which
connect matter with animal life may be as in-
finitely varied as those which regulate material
existence ? The little we know, might, per-
haps, lead us to infer a far more unlimited
field of choice. The chemist has reduced all
the materials of the earth with which we
are acquainted, to about fifty simple bodies ;

AGAINST FATE. 61

but the zoologist can make no such reductions
in his science. He must claim for one scarcely
noticed class — that of intestinal parasites —
about thirty thousand species ; and, not to
mention the larger classes of animals, who shall
number the species of infusoria in living waters,
still less those which are extinct, and whose
scarcely visible relics are contained within the
earth, in almost mountain masses.*

In absolute ignorance of any — even the
smallest link of those chains which bind life
to matter, or that still more miraculous one,
which connects mind to both, we can only
pursue our path by the feeble light of analogy,
and humbly hope that the Being, whose power

* Professor Ehrenberg, of Berlin, has discovered that the
tripoli employed in that city for polishing metals, which is
dug up at Bilin, in Bohemia, consists almost entirely of the
siliceous remains of infusoria, of a species so minute, that
about 41,000 millions of them weigh 220 grains, and oc-
cupy the space of a cubic inch. The reader will find a
translation of the highly interesting papers of Professor
Ehrenberg, in the third number of the " Scientific Me-
moirs," published by Mr. R. Taylor.

62 ARGUMENT AGAINST FATE.

and benevolence are unbounded, may enable
us, in some further stage of our existence, to
read another page in the history of his mighty
works.

Enough, however, and more than enough,
may be gathered even from our imperfect
acquaintance with matter, and some few of its
laws, to prove the unbounded knowledge
which must have preceded their organization.

ACCOUNT OF THE CREATION. 63

CHAP. IV.

ON THE ACCOUNT OF THE CREATION, IN THE FIRST
CHAPTER OF GENESIS.

A STRANGE and singular argument has fre-
quently been brought against the truth of the
facts presented to us by Geology, — facts which
every instructed person may confirm by the
evidence of his senses. It has been stated
that they cannot be true ; because, if admitted,
they lead inevitably to the conclusion, that the
earth has existed for an enormous period,
extending, perhaps, over millions of years ;
whereas, it was supposed, from the history of
the creation as delivered by Moses, that the

64 MOSAIC ACCOUNT

earth was first created about six thousand
years ago.

A different interpretation has been lately
put upon that passage of the sacred writings ;
and, according to the highest authorities of
the present time, it was not the intention of
the writer of the book of Genesis to assign this
date to the creation of our globe, but only to
that of its most favoured inhabitants.

Now, it is obvious that additional observations,
and another advance in science, may at no
distant period render necessary another inter-
pretation of the Mosaic narrative ; and this
again, at a more remote time, may be superseded
by one more in accordance with the existing
knowledge of that day. And thus, the authority
of Scripture will be gradually undermined by
the weak though well-intentioned efforts of its
friends in its support. For it is clear that
when a work, translated by persons most
highly instructed in its language, and seeking.

OF THE CREATION. 65

in plainness and sincerity, to understand its
true meaning, admits of such discordant inter-
pretations, it can have httle authority as a
history of the past, or a guide to the future.

It is time, therefore, to examine this ques-
tion by another hght, and to point out to
those who support what is called the literal
interpretation of Scripture, the precipice to
which their doctrines, if true, would inevitably
lead ; and to show, not by the glimmerings of
elaborate criticism, but by the plainest prin-
ciples of common sense, that there exists no
such fatal collision between the words of Scrip-
ture and the facts of nature.

And first, let us examine what must of
necessity be the conclusion of any candid
mind from the mass of evidence presented to
it. Looking solely at the facts in which all
capable of investigation agree — facts which it
is needless to recite, they having been so fully
and ably stated in the works of Mr. Lyell and

MOSAIC ACCOUNT

Dr. Buckland, — we there see, and with no
theoretic eye, the remains of animated beings,
more and more differing from existing races, as
we descend in the series of strata. Not merely
are the petrified bones preserved, displaying
marks of the insertion of every muscle neces-
sary for the movement of the living animal,
but in some cases we discover even the secre-
tions of their organs, prepared either for nou-
rishment or for defence. Almost every stratum
we pause to examine, affords indubitable evi-
dence of having, at some former period, existed
for ages at the bottom of some lake or estuary,
some inland sea, or some extensive ocean
teeming with animal existence, or of having
been the surface of a country covered with
vegetation, which perished and was renewed
at distant and successive periods.

Those, however, who, without the know-
ledge which enables them to form an opinion
on the subject, feel any latent wish that this
evidence should be overthrown, would do

OF TIIK CREATION. G?

well to remember that geology also furnishes
strong evidence in favour of the much more
direct statement of Moses, as to the recent
creation of man. And although we must ever
feel a certain degree of caution in admitting
negative evidence as conclusive ; yet, in the
present instance, the multitude of fossil bones
which have been discovered, and which, when
examined by persons dult/ qualified for the
task, have been uniformly pronounced to be
those of various tribes of animals, and not
those of the human race, undoubtedly affords
strong corroborative evidence in confirmation
of the Mosaic account.

In truth, the mass of evidence which combines
to prove the great antiquity of the earth, is so
irresistible, and so unshaken by any opposing
facts, that none but those who are alike inca-
pable of observing the facts and of appreciating
the reasoning, can for a moment conceive the
present state of its surface to have been the
result of only six thousand years of existence.

F 2

68 MOSAIC ACCOUNT

What, then, have those accomplished who
have restricted the Mosaic account of creation
to that diminutive period, which is, as it were,
but a span in the duration of the earth's ex-
istence, and who have imprudently rejected
the testimony of the senses, when opposed to
their philological criticisms ? Undoubtedly, if
they have succeeded in convincing either them-
selves or others, that one side of the question
must be given up as untenable ; those who
are so convinced are bound to reject that
which rests on testimony, not that which is
supported by still existing facts. The very
argument which Protestants have opposed to
the doctrine of transubstantiation,* would, if

* The historian of the " Decline of the Roman Empire,"
carried the argument yet further ; —

*' I still remember (he remarks) my solitary transport at
" the discovery of a philosophical argument against tran-
*' substantiation ; that the text of Scripture which seems to
" indicate the real presence is attested only by a single
" sense — our sight ; while the real presence itself is disproved
" bv three of our senses — the sight, the touch, the taste." —
Gibbon s Memoirs of his Life, vol. i. p. 58.

01' THE CREATION.

theii' vlex& of the case were correct, be equally
irresistible against the book of Genesis.

But let us consider what would be the con-
clusion of every reasonable being in a parallel
case. Let us imagine a manuscript written
three thousand years ago, and professing to
be a revelation from the Deity, in which it
was stated that the colour of the paper of the
very book now in the reader's hands is black,
and that the colour of the ink in the charac-
ters which he is now reading is white : — with
that reasonable doubt of his own individual
faculties which would become the inquirer into
the truth of a statement said to be derived from
so high an origin, he would ask of all those
around him, whether to their senses the paper
appeared to be black and the ink to be white.
If he found the senses of other individuals
agree with his own, then he would undoubt-
edly pronounce the alleged revelation a for-
gery, and those who propounded it to be either
deceived or deceivers. He would rightly im-

70 MOSAIC ACCOUNT

pute the attempted deceit to moral turpitude,
to the gross ignorance or to the interested mo-
tives of the supporters of it ; and he certainly
would not commit the impiety of supposing the
Deity to have wrought a miraculous change
upon the senses of our whole species, and to
demand their belief in a fact directly opposed
to those senses — thus throwing doubt upon •
every conclusion of reason which related to
external objects, and amongst others, upon the
very evidence by which the authenticity of that
questionable manuscript was itself supported,
and even of its very existence when before
their eyes.

Thus, then, had those who attempt to show
that the account of the creation, in the book of
Genesis, is contradicted by the discoveries of
modern science, succeeded, they would have
destroyed the testimony of Moses — they would
have uncanonised one portion of Scripture, and
by implication have thrown doubt on the re-
mainder. But minds which thus failed to trace

OF THE CREATION. 71

out the necessary consequences of their own
argument, were not Hkely to have laid very
secure foundations for the basis on which it
rested ; and I shall presently prove that the
contradiction they have imagined can have no
real existence ; and that whilst the testimony
of Moses, remains unimpeached, we may also
be permitted to confide in the testimony of
our senses.

72 MOSAIC ACCOUNT

CHAP. V.

FURTHER VIEW OF THE SAME SUBJECT.

Before entering on the main argument it
may be remarked, that the plainest and most
natural view of the language employed by the
sacred historian of the earth is, that his ex-
pressions ought to be received by us in the
sense in which they were understood by the
people to whom he addressed himself. If, when
speaking of the creation, instead of using the
terms light and water, he had spoken of the
former as a wave, and of tlie latter as the union
of two invisible airs, he would assuredly have

OF THE CREATION. 73

been perfectly unintelligible to bis country-
men. At the distance of above three thousand
years his writings would just have begun to be
comprehended, and possibly three thousand
years hence those views may be as inappli-
cable to the then existing state of human
knowledge as they would have been when the
first chapter of Genesis was written.

Those, however, who attempt to disprove
the facts presented by observation, by placing
them in opposition to revelation, have mistaken
the very groundwork of the question. The
revelation of Moses itself rests, and must ne-
cessarily rest, on testimony. Moses, the author
of the oldest of the sacred books, lived about
fifteen hundred years before the christian era,
or about three thousand three hundred years
ago. The oldest manuscripts of the Pentateuch
at present known, appear to have been written
about 900 years ago.* These were copied from

* Mr. Home, in the Introduction to the Critical Study of

MOSAIC ACCOUiNT

others of older date, and those again might
probably, if their history were known, be traced
up through a few transcripts to the original

the Holy Scriptures, states, that the total number of He-
brew MSS. collated by Dr. Kennicott, for his critical edi-
tion of the Hebrew Bible, was about 630. In that work,
Mr. Home gives an account of ten of the most ancient of
these MSS. : three of which contain the first chapter of
Genesis, viz. : —

No. 4. Codex Caesenae, in the Malatesta Library at

Bolosrna, written about the end of the eleventh century.

No. 6. Codex Mediolanensis, written towards the close

of the twelfth century. " The beginning of the book of

'' Genesis, and the end of Leviticus and Deuteronomy,

** have been written by a later hand."

No. 8. Codex Parisiensis, 27, about the commencement

of the twelfth century.
No. 10. Codex Parisiensis, 24, written at the beginning
of the twelfth century.

In the same work is an account of six of the most ancient
of the four hundred and seventy-nine collated by M. De
Rossi. Two of these contain the first chapter of Ge-
nesis ; and the date of both is about the end of the eleventh
or beginning of the twelfth century.

Of the Manuscripts of the Samaritan versions of the Pen-
tateuch, cited in the same work— one the Codex 197, in
the Ambrosian Library at Milan — Dr. Kennicott thinks that
it is certainly not later than the tenth century.

or THE CREA'IION.

author ; but no part of this is revelation ; it is
testimony. Although the matter which the
book contains was revealed to Moses, the fact
that what we now receive as revelation is
the same with that originally communicated
revelation, is entirely dependent on testimony.
Admitting, however, the full weight of that
evidence, corroborated as it is by the Samaritan
version ; nay, even supposing that we now
possessed the identical autograph of the book
of Genesis by the hand of its author, a most
important question remains, — What means do
we possess of translating it ?

In similar cases we avail ourselves of the
works of the immediate predecessors, and of
the contemporaries of the writer ; but here we
are acquainted with no work of any prede-
cessor,— of no writing of any contemporary ;
and we do not possess the works of any
writers in the same language, even during se-
veral succeeding centuries, if we except some
few of the sacred books. How, then, is it

76 MOSAIC ACCOUNT

possible to satisfy our minds of the minute
shades of meaning of words, perhaps employed
popularly ; or, if they were employed in a
stricter and more philosophical sense, where
are the contemporary philosophical writings
from which their accurate interpretation may
be gained ?

The extreme difficulty of such an inquiry
will be made apparent by imagining a parallel
case. Let us suppose ail writings in the
English, and indeed in all other languages pre-
vious to the time of Shakespeare, to have been
destroyed ; — let us imagine one manuscript of
his plays to remain, but not a vestige of the
works of any of his contemporaries; and further,
suppose, the whole of the succeeding works of
English literature to be annihilated nearly up
to the present time. Under such circumstances,
what would be our knowledge of Shakespeare ?
We should undoubtedly understand the ge-
neral tenor and the plots of his plays. We
should read the language of all his characters ;

OF Tin: CKI.ATION.

and viewing it generally, we might even be
said to understand it. But how many words
connected with the customs, habits, and man-
ners of the time must, under such circum-
stances, necessarily remain unknown to us !
Still further, if any question arose, requiring
for its solution a knowledge of the minute
shades of meaning of words now long obsolete,
or of terms supposed to be used in a strict or
philosophical sense, how completely unsatis-
factory must our conclusions remain ! Such
I conceive to be the view which common sense
bids us take of the interpretation of the book
of Genesis. The language of the Hebrews,
in times long subsequent to the date of that
book, may not have so far changed as to pre-
vent us from rightly understanding generally
the history it narrates ; but there appears to
be no reasonable ground for venturing to pro-
nounce with confidence on the minute shades
of meaning of allied words, and on such foun-
dations to support an argument opposed to the
evidence of our senses.

78 MOSAIC ACCOUNT

I sliould have hesitated in offering these
remarks respecting the right interpretation of
the Mosaic account of the creation, had the ar-
gument depended on any acquaintance with the
language in which the sacred volume is writ-
ten, or on any refinements of criticism, had
I possessed that knowledge ; but in estimating
its validity, or in supplying a more cogent
argument, I intreat the reader to consider
well the difficulties which it is necessary to
meet.

1st. The Church of England, if we may
judge by the writings of those placed in autho-
rity, has hitherto considered it to have been
expressly stated in the book of Genesis, that
the earth was created about six thousand
years ago.

2dly. Those observers and philosophers
who have spent their lives in the study of
Geology, have arrived at the conclusion that
there exists irresistible evidence, that the date

OF THE CREATION. 79

of the earth's first formation is far anterior to
the epoch supposed to be assigned to it by
Moses ; and it is now admitted by all compe-
tent persons, that the formation even of those
strata which are nearest the surface must have
occupied vast periods — probably millions of
years — in arriving at their present state.

3dly. Many of the most distinguished mem-
bers of the Church of England now distinctly
and formally admit the fact of such a length-
ened existence of the earth we inhabit ; for it
is so stated in the eighth Bridgewatei^ Treatise,
a work written by the Professor of Geology in
the University of Oxford — himself holding an
office of dignity in that Church, and expressly
appointed to write upon that subject, by the
Archbishop of Canterbury, and the Bishop of
London.

4thly, Tlie Professor of Hebrew at the same
University has proposed a new interpretation
of those passages of the Book of Genesis,

80 MOSAIC ACCOUNT

which were hitherto supposed to be adverse to
the now admitted facts.

Such being the present state of the case ; —
it surely becomes a duty to require a very high
degree of evidence, before we again claim au-
thority for the opinion that the book of Genesis
contains such a precise account of the work of
the creation, that we may venture to appeal to
it as a refutation of observed facts. The history
of the past errors of our parent Church sup-
plies us with a lesson of caution which ought
not to be lost by its reformed successors.
The fact that the venerable Galileo was com-
pelled publicly to deny, on bended knee, a
truth of which he had the most convincing de-
monstration, remains as a beacon to all after
time, and ought not to be without its influence
on the inquiring minds of the present day.

If the explanation offered by the Pro-
fessor of Hebrew be admitted, those who
adhere to it must still have some misgivings

OF THE CREATION. 81

as to the effect of new discoveries in nature
causing continual occasion for amended trans-
lations of various texts ; whereas, should the
view which has been advocated in this chap-
ter be found correct, instead of fearing that the
future progress of science may raise additional
difficulties in the way of revealed religion,
we are at once relieved from all doubt on that
subject.

THE DESIRE

CHAP. VI.

OF THE DESIRE OF IMMORTALITY.

That wish, universally expressed in every
variety of form, of remaining in the memory
of our fellow-creatures after our passage from
the present scene, has rightly been adduced as
evidence of the desire of immortality, and has
sometimes been explained as being founded on
an instinctive belief that we are destined to
it by the Creator.

The hope of remaining embalmed in the
fond recollection of those we held most dear
in life, and even of being remembered by our

OF IMMORTALITY. 83

more immediate descendants, has something
in it nearly connected with self; but the wish
for more extended reputation, — the desire that
our name should pass in after times from
mouth to mouth, cherished and admired by
those whose applause is won by no personal
recollections : or the still more fervent aspira-
tions, that we may stamp indelibly on the age
we live in some mark of our individual exist-
ence which shall form an epoch in the history
of man : these hopes, these longings, receive
no interpretation from the all-dominant prin-
ciple of self ; unless indeed we suppose the
sentient principle of our nature not merely
existing, but also conscious of, and gratified
by, the earthly immortality it had achieved.
Yet the more distant and the higher the objects
we pursue, the less is it possible to suppose the
mind, so occupied on earth, can, in another
stage of its existence, derive pleasure from such
perceptions.

To support this opinion, it is only necessary

G 2

84 THE DESIRE

to examine the states of mind in the various
classes of the aspirants after fame .

Through every form of society, and through
every rank of each, may be traced this uni-
versal passion. Examine the most highly civi-
lized inhabitants of earth ; search through it
for the most cultivated and refined in taste ;
for the most sagacious in penetrating the pas-
sions of mankind, the most skilful in wielding
them, or the most powerful in intellectual
might. Taste, feeling, passion, ambition, ge-
nius, severed or combined, equally yield obedi-

OF IMMORTALITY. 85

ence to its sway, and present, under different
appearances, the effects of its all-controlling
power.

Look at the highest productions of the poet
or the novelist. By connecting his story with
the scenery, the traditions, or the history of
his country, he may ensure for it a local inte-
rest, a domestic and transitory popularity ; but
it is that deeper penetration into the secrets
of the human heart, which enables him to
select from amongst the same materials, those
feelings that are common to the race which

86 THE DESIRE

have, as occasion called them forth, appeared,
and will continue to reappear, as long as the
same affections and passions shall continue to
animate and agitate our frames.

From the examination of these its highest
forms, we may gather some common principles,
and be enabled to perceive that the love of
fame is far different from that passion for vul-
gar applause with which it is too frequently

OF IMMORTALITY. 87

confounded. We may learn, that the higher
the intellectual powers devoted to the task,
the more remote the period for which ambition
delights to raise its far distant altar.

88 ON TIME.

CHAP. VII.

ON TIME.

Time and change are great, only with re-
ference to the faculties of the beings which
note them. The insect of an hour, which
flutters, during its transient existence, in an
atmosphere of perfume, would attribute un-
changing duration to the beautiful flowers
of the cistus, whose petals cover the dewy

ON TIME.

grass but a few hours after it has received
the Hfeless body of the gnat. These flowers,
could they reflect, might contrast their trans-
itory hves with the prolonged existence of
their greener neighbours. The leaves them-
selves, counting their brief span by the lapse
of a few moons, might regard as almost
indefinitely extended the duration of the com-
mon parent of both leaf and flower. The
lives of individual trees are lost in the con-
tinued destruction and renovation which take
place in forest masses. Forests themselves,
starved by the exhaustion of the soil, or con-
sumed by fire, succeed each other in slow
gradation. A forest of oaks waves its lux-
uriant branches over a spot which has been
fertilized by the ashes of a forest of pines.
These periods again merge into other and still
longer cycles, during which the latest of a
thousand forests sinks beneath the waves, from
the gradual subsidence of its parent earth ; or in
which extensive inundations, by accumulating
the silt of centuries, gradually convert the

90 ON TIME.

living trunks into their stony resemblances.
Stratum upon stratum subsides in comminuted
particles, and is accumulated in the depths of
the ocean, whence they again arise, consoli-
dated by pressure or by fire, to form the con-
tinents and mountains of a new creation.

Such, in endless succession, is the history of
the changes of the globe we dwell upon ; and
human observation, aided by human reason,
has as yet discovered few signs of a be-
ginning— no symptom of an end. Yet, in
that more extended view which recognises
our planet as one amongst the attendants of
a central luminary ; that sun itself the soul,
as it were, of vegetable and animal existence,
but an insignificant individual among its
congeners of the milky way : — when we re-
member that that cloud of light, gleaming
with its myriad systems, is but an isolated
nebula amongst a countless host of rivals,
which the starry firmament surrounding us
on all sides, presents to us in every varied

ON TIME. 91

form ; — some as uncondensed masses of atte-
nuated light; — some as having, in obedience
to attractive forces, assumed a spherical figure ;
others, as if farther advanced in the history of
their fate, having a denser central nucleus
surrounded by a more diluted light, spreading
into such vast spaces, that the w^hole of our
own nebula would be lost in it : — others there
are, in which the apparently unformed and
irregular mass of nebulous light is just curd-
ling, as it were, into separate systems ; w^hilst
many present a congeries of distinct points of
light, each, perhaps, the separate luminary of
a creation more glorious than our own ; — when
the birth, the progress, and the history of
sidereal systems are considered, we require
some other unit of time than even that com-
prehensive one which astronomy has unfolded
to our view. Minute and almost infinitesimal
as is the time which comprises the history of
our race compared with that which records
the history of our system, the space even of

92 ON TIME.

this latter period forms too limited a stan-
dard wherewith to measure the footmarks of
eternity.

CHAP. VIIL

ARGUMENT FROM LAWS INTERMITTING ON THE
NATURE OF MIRACLES.

The object of the present chapter is to
show that miracles are not deviations from
the laws assigned by the Almighty for the
government of matter and of mind ; but that
they are the exact fulfilment of much more
extensive laws than those we suppose to
exist. In fact, if we were endued with
acuter senses and higher reasoning faculties,
they are the very points we should seek to
observe, as the test of any hypothesis we had
been led to frame concerning the nature of

94 LAWS INTERMITTING.

those laws. Even with our present imperfect
faculties we frequently arrive at the highest
confirmation of our views of the laws of na-
ture, by tracing their actions under singular
circumstances.

The mode by which I propose to arrive at
these conclusions is, by appealing to the judg-
ment which each individual will himself form,
when examining that piece of mere human
mechanism, to which the argument so fre-
quently compels me to advert. If he shall
agree with me, that the second of the two
views presented to him exhibits a higher de-
gree of knowledge, and a higher exertion of
power, than the first, he must inevitably con-
clude, that the view here taken of the nature
of a miracle, assigns a far higher degree of
power and knowledge to the Deity.

Let the reader again imagine himself sit-
ting before the calculating engine, and let him
again observe and ascertain, by lengthened

NATURE OF MIRACLES. 95

induction, the nature of the law it is com-
puting. Let him imagine that he has seen
the changes wrought on its face by the lapse of
thousands of years, and that, without one soli-
tary exception, he has found the engine regis-
ter the series of square numbers. Suppose,
now, the maker of that machine to say to the
observer, '^ I will, by moving a certain mecha-
'' nism, which is invisible to you, cause the
*^ engine to make a cube number instead of a
*^ square one, and then to revert to its former
*' course of square numbers;" the observer would
be inclined to attribute to him a degree of
power but little superior to that which was
necessary to form the original engine.

But, let the same observer, after the same
lapse of time — the same amount of uninter-
rupted experience of the uniformity of the law
of square numbers, hear the maker of that en-
gine say to him — '* The next number which
" shall appear on those wheels, and which
*' you expect to find a square number, shall

96 LAWS INTERMITTING.

' not be such. When the machine was ori-
' ginally ordered to make these calculations,
^ I impressed on it a law, which should coin-
' cide with that of square numbers in every
^ case, except the one which is now about to
' appear, after which no future exception can
' ever occur ; but the unvarying law of the
' squares shall be pursued until the machine
' itself perishes from decay."

Undoubtedly the observer would ascribe a
greater degree of power to the artist who thus
willed that event at the distance of ages before
its arrival.

If the contriver of the engine then explain
to him, that, by the very structure of it, he has
power to order any number of such apparent
deviations from its laws to occur at any future
periods, however remote, and that each of
these may be of a different kind ; and, if he
also inform him, that he gave it that structure
in order to meet events, which he foresaw must

NATURE OF MIRACLES. 07

happen at those respective periods, there can
be no doubt that the observer would ascribe to
the inventor far higher knowledge than if,
when those events severally occurred, he were
to intervene, and temporarily alter the calcu-
lations of the machine.

If, besides this, he were so far to explain the
structure of the engine that the observer could
himself, by some simple process, such as the
mere moving of a bolt, call into action those
apparent deviations whenever certain com-
binations were presented to his eye; if he
were thus to impart a power of predicting
such excepted cases, dependent on the will,
although otherwise beyond the limits of the
observer's power and knowledge, such a struc-
ture would be admitted as evidence of a still
more skilful contrivance.

The engine which, in a former chapter, I
introduced to the reader, possesses these
powers. It may be set, so as to obey by any

98 LAWS INTERMITTING.

given law ; and, at any periods, however re-
mote, to make one or more seeming exceptions
to that law. It is, however, to be observed,
that the apparent law which the spectator ar-
rived at, by an almost unlimited induction, is
not the full expression of the law by which the
machine acts ; and that the excepted case is
as absolutely and irresistibly the necessary
consequence of its primitive adjustment, as is
any individual calculation amongst the count-
less multitude.

When the construction of that engine was
first attempted, I did not seek to give to it
the power of making calculations so far be-
yond the reach of mathematical analysis as
these appear to be : nor can I now foresee
a probable period at which they may become
practically available to human wants. I had
determined to invest the invention with a de-
gree of generality which should include a wide
range of mathematical power ; and I was well
aware that the mechanical generalisations

NATURE OF MIRACLES. 99

I had organised contained within them much
more than I had leisure to study, and some
things which will probably remain unpro-
ductive to a far distant day.

Amongst those combinations which I was
induced to examine, I observed the powers I
have now recorded ; and the reflections they
produced in my own mind, impelled me to pur- i p

sue them for a time. If the reader agree with ^^^4^ .
me in opinion, that these speculations have led / r
to a more exalted view of the great Author of . ^

the universe than any we yet possessed, he ^,| wv^^/<r» ^
must also have arrived at the conclusion, that ^ , * .^ ,
the study of the most abstract branch of prac- ^^ ^ ^
tical mechanics, combined with that of the ^
most abstruse portions of mathematical science,
has no tendency to incapacitate the human '' ^^ c^«^4^:
mind from the perception of the evidences of ^/^ y^^-
natural religion ; and that even those very ^

sources themselves furnish arguments which ^t<>^v-^^
have opened more splendid views of the gran- rK^^

deur of creation than any which the sciences

H 2

100 LAWS INTERMITTING.

of observation or of physics have yet sup-
plied.

It may not, perhaps, be without its use to
suggest another illustration respecting the na-
ture of miracles. It is known that mathema-
tical laws are sometimes expressed by curves.
The figure 1 represents a re-entering curve of
four dimensions, whose law of formation is
given in the note.* A slight change in the na-
ture of the constants makes it assume the form
of fig. 2, which is still a continuous curve ; but
a further change of the constants causes it to
have two ovals, quite disconnected from the
larger portion ; and, as the constants again
alter, these ovals are reduced to points.

* The equation

2/'' — 4 y^ = — ax!^ H- hx^ + cx^ -\- dx -\- e
expresses several figures of an oval form, according to the
nature of the roots of the equation,

— ax^ + hx^ '\-cx^ -\- dx -\- e=^o.
If its two lesser roots become imaginary, the curves, figures
1, 2, 3, are produced.

NATURE OF MIRACLES.

101

Fig. I.

Fig. 2.

Fig.S.

Fig. 4.

NATURE OF MIRACLES.

101

In all four cases, every point in each branch
of the curve obeys the same general law. The
points, P and Q, invisible to the eye, are yet
detected by mathematical analysis, and fulfil
as precisely the original equation as any of the
infinite number of other points, which consti-
tute the rest of the curve. These points might
be situated on the curve itself, and they are
well known to mathematicians. It is to these
singular points, which really fulfil the law of
the curve, but which present to those who
only judge of them by the organ of sight
an apparent discontinuity, that I wish to
call the attention, as offering an illustration
of the doctrine here explained respecting
miracles.

It has been remarked, in the beginning of
the present chapter, that it is to the singular
points — to those points of such infinitely rare
occurrence in a curve — that we frequently have
recourse, as the test of our theories, for ex-
plaining the phenomena of nature.

104 LAWS INTERMITTING.

The existence, under peculiar circumstances,
of conical refraction, was predicted by Sir W.
Hamilton ; and, from an analytical investiga-
tion into the nature of the curve surface, which
represents the form of the lurainiferous wave
within the crystal, he ascertained that it had
four conoidal cusps, at each of which there were,
consequently, an infinite number of tangent
planes. The course of the refracted ray being
determined by the tangent plane to the wave
surface, it followed that a single ray within the
crystal, transmitted in the direction of the line
joining two opposite cusps, corresponded to an
infinite number of refracted rays without, con-
stituting a refracted cone.

The second case of conical refraction, pre-
dicted by Sir William Hamilton, depended on
another mathematical fact — namely, that the
wave surface is touched in an infinite number
of points, constituting a small circle of contact,
by a single plane parallel to one of the circu-
lar sections of the surface of elasticity.

NATURE OF MIRACLES. 105

Professor Lloyd undertook to make the very
delicate experiments required for this most
interesting subject. Of the great importance
of this investigation. Professor Lloyd was fully
aware, for he remarks —

'' Here, then, are two singular and unex-
" pected consequences of the undulatory theory,
*' not only unsupported by any facts hitherto
observed, but even opposed to all the analo-
gies derived from experience. If confirmed
"by experiment, they would furnish new and
'' almost convincing proofs of that theory ;
*' and, if disproved, on the other hand, it is
" evident that the theory must be abandoned
" or modified.*

On examining the first of these cases, expe-
rimentally, the fact of conical refraction was
fully established. But a new result now pre-
sented itself: the rays of light thus conically

* Trans, of Royal Irish Academy, Vol. XVII.

€(

((

106 LAWS INTERMITTING.

refracted were found to be polarized ; and it
was observed^ that ''the angle between the
" planes of polarization of any two rays of
'' the cone was half the angle between the
'' planes, containing the rays themselves, and
'' the axis."

This new law, thus approximately obtained
by experiment, led the observer back to the
theory ; and, on a further examination, he de-
tected in that theory the very law he had just
discovered by observation.

The second case of conical refraction re-
quired experiments of a still more delicate
nature. They were, however, made, and suc-
ceeded equally. The conically refracted ray
was found to be polarised, according to the law
which, in this instance, analysis had predicted ;
and, to complete the triumph of this union of
theory and experiment, the measures in both
cases, when made under proper circumstances,
accorded with the theoretical conclusions.

NATUllE^ OF MIRACLES. 107

within such limits as might be fairly attributed
to the necessary errors of observation.

It is worthy of remark, that, at first, two
facts presented themselves, which seemed at
variance with the theory. In the first place, the
emergent rays formed a sohd cone, instead of
a conical surface ; and, in the second place, the
calculated angle, subtended by the sides of the
cone, was only one half the observed angle.
Both the facts were shown to depend upon
the size of the aperture, and to arise from the
rays which were inclined at small angles to the
single theoretical direction. When the aper-
ture was diminished, so as to be vei^y small, (the
case calculated by Sir William Hamilton,) then
the cone of light became a conical surface, and
the observed angle was the same as the calcu-
lated one.*

* Those who are acquainted with the history of astronomy,
cannot fail to recall a parallel discrepancy between observa-
tion and calculation in the theory of gravity. It appeared
to result from that law, that the motion of the moon's

108 NATURE OF MIRACLES.

apogee was only one half of what observation proved it to be ;
and it is singular that Euler, D'Alembert, and Clairaut
arrived, by different methods, at the same erroneous result ;
and the truth of the great law of gravity appeared for a time
to be doubtful. Clairaut, however, having assumed that
the law of gravity contained a term only sensible at small
distances (such as that of the moon), re-calculated the ques-
tion, and finding it necessary, in consequence of this terra, to
push his approximation further than he had done, arrived
at the conclusion, that the co-efficient of the new term va-
nished ; and also, that the simple law of the inverse square
of the distance, when the approximations were sufficiently
pursued, gave the whole motions which observations had
discovered.

PERMANENT IMPRESSION OF WORDS. 109

CHAP. IX.

ON THE PERMANENT IMPRESSION OF OUR WORDS
AND ACTIONS ON THE GLOBE WE INHABIT.

The principle of the equality of action and
reaction, when traced through all its conse-
quences, opens views which will appear to many
persons most unexpected.

The pulsations of the air, once set in motion
by the human voice, cease not to exist with
the sounds to which they gave rise. Strong
and audible as they may be in the immediate
neighbourhood of the speaker, and at the
immediate moment of utterance, their quickly

110 THE PERMANENT IMPRESSION

attenuated force soon becomes inaudible to
human ears. The motions they have impressed
on the particles of one portion of our atmo-
sphere, are communicated to constantly in-
creasing numbers, but the quantity of motion
measured in the same direction receives no
addition. Each atom loses as much as it
gives, and regains again fiom others, portions
of those motions which they in turn give up.

The vs^aves of air thus raised, perambulate
the earth and ocean's surface, and in less than
twenty hours every atom of its atmosphere
takes up the altered movement due to that
infinitesimal portion of the primitive motion
which has been conveyed to it through count-
less channels, and which must continue to in-
fluence its path throughout its future exist-
ence.*'

* La courbe decrite par une simple molecule d'air ou
vapeurs est reglee d'une maniere aussi certain que les
orbites planetaires : il n'y a de difference entre elles, que

OF OUR WOllDS. Ill

But these aerial pulses, unseen by the
keenest eye, unheard by the acutest ear, un-
perceived by human senses, are yet demon-
strated to exist by human reason ; and, in some
few and hmited instances, by calling to our
aid the most refined and comprehensive in-
strument of human thought, their courses are
traced and their intensities are measured. If
man enjoyed a larger command over mathe-
matical analysis, his knowledge of these mo-
tions would be more extensive ; but a being
possessed of the unbounded knowledge of that
science, would trace every the minutest conse-
quences of that primary impulse. Such a
being, however far exalted above our race,
would yet be immeasurably below even our
conception of infinite intelligence ; yet by him,
supposing the original conditions of each atom
of the atmosphere, as well as all the extraneous
causes acting upon it to be given, its future and
inevitable path would be clearly traced ; and

celle qu'y met notre ignorance. — La Place^ Theorie Ana-
lytique des Probabilites. Int. p. iv.

112 THE PERMANENT IMPRESSION

supposing the interference also of no new
causes, the circumstances of the future history
of the whole of the earth's atmosphere would
be distinctly seen, and might be absolutely
predicted for any even the remotest point of
time. *

Let us imagine a being, invested with such
knowledge, to arrive at the predicted moment.
If any the slightest deviation exists, he will
immediately read in its existence the action
of a new cause ; and, through the aid of the
same analysis, tracing this discordance back
to its source, he would become aware of the
time of its commencement, and the point of
space at which it originated.

Thus considered, what a strange chaos is
this wide atmosphere we breathe! Every
atom impressed with good and with ill, re-
tains at once the motions which philosophers

* See Note C in the Appendix.

OF OUR WORDS. 113

and sages have imparted to it, mixed and
combined in ten thousand ways with all that is
worthless and base. The air itself is one vast
library, on whose pages are for ever written all
that man has ever said or even whispered.
There, in their mutable but unerring charac-
ters, mixed with the earliest, as well as the
latest sighs of mortality, stand for ever re-
corded, vows unredeemed, promises unfulfilled,
perpetuating in the united movements of each
particle, the testimony of man's changeful
will.

But if the air we breathe is the never-failing
historian of the sentiments we have uttered,
earth, air, and ocean, are in like manner the
eternal witnesses of the acts we have done. The
same principle of the equality of action and
reaction applies to them : whatever motion is
communicated to any of their particles, is trans-
mitted to all around it, the share of each being
diminished by their number, and depending
jointly on the number and position of those

IH THE PERMANENT IMPRESSION

acted upon by the original source of disturbance.
The waves of air, although in many instances
sensible to the organs of hearing, are only ren-
dered visible to the eye by peculiar contriv-
ances ; whilst those of water offer to the sense
of sight the most beautiful illustration of the
transmission of motion. Every one who has
thrown a pebble into the still waters of a shel-
tered pool, has seen the circles it has raised
gradually expanding in size, and as uniformly
diminishing in distinctness. He may have ob-
served the reflection of those waves from the
edges of the pool. He may also have noticed
the perfect distinctness with which two, three,
or more series of waves each pursues its own
unimpeded course, when diverging from two,
three, or more centres of disturbance. He may
have observed, that in such cases the particles
of water where the waves intersect each other,
partake of the movements due to each series.

No motion impressed by natural causes, or
by human agency, is ever obliterated. The

OP OUR WORDS. 115

ripple on the ocean's surface caused by a gentle
breeze, or the still water which marks the more
immediate track of a ponderous vessel gliding
with scarcely expanded sails over its bosom,
are equally indelible. The momentary waves
raised by the passing gale, apparently born but
to die on the spot which saw their birth, leave
behind them an endless progeny, which, reviv-
ing with diminished energy in other seas, and
visiting a thousand shores, reflected from each
and perhaps again partially concentrated, pursue
their ceaseless course till ocean be itself anni-
hilated.

The track of every canoe, of every vessel
which has yet disturbed the surface of the
ocean, whether impelled by manual force or
elemental power, remains for ever registered
in the future movement of all succeeding par-
ticles which may occupy its place. The furrow
which it left is, indeed, instantly filled up by
the closing waters ; but they draw after them
other and larger portions of the surrounding

116 THE PERMANENT IMPRESSION

element, and these again once moved, com-
municate motion to others in endless succes-
sion.

The solid substance of the globe itself, whe-
ther we regard the minutest movement of the
soft clay which receives its impression from the
foot of animals, or the concussion produced
from falling mountains rent by earthquakes,
equally retains and communicates, through all
its countless atoms, their apportioned shares of
the motions so impressed.

Whilst the atmosphere we breathe is the ever-
living witness of the sentiments we have uttered,
the waters, and the more solid materials of the
globe, bear equally enduring testimony of the
acts we have committed.

If the Almighty stamped on the brow of the
earliest murderer, — the indelible and visible
mark of his guilt, — he has also established laws
by which every succeeding criminal is not less

OF OUR WORDS. 117

irrevocably chained to the testimony of his
crime ; for every atom of his mortal frame,
through whatever changes its severed particles
may migrate, will still retain, adhering to it
through every combination, some movement
derived from that very muscular effort, by
which the crime itself was perpetrated.

118 hume's argument

CHAP. X.

ON hume's argument against miracles.

Few arguments have excited greater atten-
tion, and produced more attempts at refutation,
than the celebrated one of David Hume, re-
specting miracles ; and it might be added,
that more sophistry has been advanced against
it, than its author employed in the whole of his
writings.

It must be admitted that in the argument, as
originally developed by its author, there exists
some confusion between personal experience
and that which is derived from testimony ; and
that there are several other points open to
criticism and objection ; but the main argu-

AGAINST MIRACLES. 119

ment, divested of its less important adjuncts,
never has, and never will be refuted. Dr.
Johnson seems to have been of this opinion,
as the follov^ing extract from his life by
Boswell proves : —

*' Talking of Dr. Johnson's unwillingness to believe ex-
traordinary things, I ventured to say —

** * Sir, you come near to Hume's argument against mira-

* cles — That it is more probable witnesses should lie, or be

* mistaken, than that they should happen.'

" Johnson. — * Why, Sir, Hume, taking the proposition

* simply, is right. But the Christian revelation is not proved

* by miracles alone, but as connected with prophecies, and

* with the doctrines in confirmation of which miracles were

* wrought.' "*

Hume contends that a miracle is a violation
of the laws of nature ; and as a firm and
unalterable experience has established these
laws, the proof against a miracle from the very
nature of the fact, is as entire as any argument
from experience can possibly be imagined.

* Boswell's Life of Johnson, Oxford, 1826. vol. iii. p. 169.

120 Hume's argument

*' The plain consequence is (and it is a general maxim
*• worthy of our attention), that no testimony is sufficient
" to establish a miracle, unless the testimony be of such a
*' kind, that its falsehood would be more miraculous than the
" fact which it endeavours to establish : and even in that case
*' there is a mutual destruction of arguments, and the superior
" only gives us an assurance suitable to that degree of force
** which remains after deducting the inferior." *

The difficulty which is frequently experi-
enced in understanding this argument, appears
to arise from the circumstance, that a double
negative is concealed under the words '* its
falsehood woulabe more miraculous than'' For
in Hume's argument the word '^ miraculous''
means improbable, although the improbability
is of a very high degree. The clause then
reads —

Its falsehood would be more improbable than ;

which is evidently equivalent to

Its truth would be less improbable than ;

which is again equivalent to

Its truth would be more probable than.
* Hume's Essays, Edinburgh, 1817, vol. ii. p. 117.

AGAINST MIRACLES. 121

Replacing this in Hume's argument, it stands
thus —

" That no testimony is sufficient to establish a miracle,
" unless tlie testimony be of such a kind, that its truth
*' would be more probable than the fact which it endea-
" vours to establish."

The argument is now reduced to the mere ^
truism, that —

The prohahllity in favour of the testimony
by which a miracle is supported, must be
greater than the prohahllity of the miracle itself. /

Before entering on the arguments I have to
offer upon this point, it will be right to recall
to the reader the view taken in a preceding
chapter concerning the nature of miracles, and
to compare it with that entertained by the
acute philosopher whose essay I am venturing
to criticise, lest, from any unperceived differ-
ence in the employment of the term, I should
inadvertently mislead both myself and my
readers.

122 Hume's argument

It has been shown in the chapter above re-
ferred to, that — A miracle may he only the
exact fulfilment of a general law of nature, under
such singular circumstances that to those imper-
fectly acquainted with that law, it appears to be
in direct opposition to it. The definition of a
miracle adopted by Hume is this —

" A miracle is a violation of the laws of nature." *

And again, in note K —

'• A miracle may be accurately defined — A transgression
^^ of a law of nature hy a particular volition of the Deity ^ or
*' hy the interposition of some invisible agent, A miracle may
*' be either discovered by men or not. This alters not its
" essence or its nature, "f

In order rightly to interpret this definition
of a miracle, it is necessary to have the author's
definition of a law of nature, which is given in
a subsequent part of his essay.

** It is exjDerience only which gives authority to human
'•* testimony ; and it is the same experience which assures us

* Page 114. . f Page 462.

AGAINST MIRACLES. 123

** of the laws of nature. When, therefore, these two kinds
*' of experience are contrary, we have nothing to do but
*' subtract the one from the other, and embrace an opinion,
** either on one side or the other, with that assurance which
" arises from the remainder."*

Having pointed out the difference in our
definitions, I shall now show a point of resem-
blance between them, which is apparent in
the following extract —

*' What we have said of miracles, may be applied without
** any variation to prophecies ; and indeed all prophecies are
** real miracles, and as such only can be admitted as proofs
** of any revelation."f

The reader who has entered into the rea-
soning of Chapter VIII. of this fragment will
perceive that, according to the views there
maintained, it might be asserted that all mira-
cles are prophecies : that they are revelations
more or less in advance of events which,
although in real accordance, are apparently in
direct contradiction to the laws of nature.

* Hume's Essay, vol. ii. p. 129.

"f Page 131. A passage in this quotation has for conve-
nience been marked in italics ; it is not so in the original.

124 hume's argument

Hume's argument in the first part of the
Essay of Miracles, seems intended to prove that
although the Deity might cause miracles to be
worked, yet that it is impossible that those
who did not witness them, could be convinced
of their having occurred by any human testi-
mony.

In the second part of that essay the author
applies a hmitation to which he requests parti-
cular attention — namely, that no human testi-
mony can have such force as to prove a mira-
cle, and make it a just foundation for any system
of religion,

*' I beg the limitations here made may be remarked,
** when I say, that a miracle can never be proved, so as to
" be the foundation of a system of religion."*

Had the argument been continued, it might
have appeared still more startling ; for, as all
miracles of which we have any account, rest, in

* Hume's Essay, vol. ii. p. 128.

AGAINST MIRACLES. 12/")

the first instance, on the testimony of eye-wit-
nesses who are not themselves ahve to deUver
their testimony, we require the fact that they
did so testify, to be confirmed to us by the testi-
mony of others. Now, if, in order to prove
the miracle, it must be a greater miracle that
the testimony of the eye-witnesses is true ; so,
in order to assure us that the eye-witnesses did
testify it, it must be a still greater miracle that
those who assure us of that fact, themselves
speak the truth. If this second testimony is not
communicated to us personally, but is again
transmitted, either through persons or through
writings, we must again, at each transmission,
require a greater miracle than at the preceding.
Thus, it might at first sight be made to appear,
that the amount of evidence required to esta-
blish the truth of a miracle, said to have been
performed at any distant period of past time,
would be enormous.

However alarming this doctrine may appear,
an examination of the real numerical value of

126 hume's argument

the quantities spoken of in Hume's argument as
greater and less, will prove, as has frequently
happened in other instances, that the con-
sequences deduced from it by no means neces-
sarily follow.

Hume has deduced the a priori probabi-
lity against the occurrence of a miracle, from
the universal experience of mankind; and,
as it is only our own entire ignorance of all
their causes which renders the question of mi-
racles one of probability, there is no objection
to be made to this step. On the contrary, it
enables us to lay the foundation of numerical
deductions, which have none of the vagueness
of those at which Hume arrived.

Taking, therefore, Hume's own mode of es-
timating a miracle, let us suppose the chances
against its occurrence to be n to 1, where
n is some enormously large number. Still,
however, in this view of the question, there is
a probability, however small, for its occurrence.

AGAINST MIRACLES. 127

whilst there exists an improbability of vast mag-
nitude against it. It is on this ground that I
have, according to Hume's own notions, called
a miracle an improbahiUty ; and we may, there-
fore, substitute that term for miracle and mi-
raculous. The argument of Hume, when so
translated, stands thus : —

That no testimony is sufficient to establish an
improbability, unless the testimony be of such a
kind that its falsehood would be more improba-
ble than the occurrence of the fact which it en-
deavours to establish.

But the '^ fact which it endeavours to es-
tablish" is the improbability mentioned in the
second line. Consequently, the testimony
must be of such a nature, that its falsehood
would be more improbable than that first im-
probability.

Let us now apply the test of number to the
argument of Hume ; and, for the sake of simpli-

128 Hume's argument

city, let us take the case of the miracle men-
tioned in the next chapter, and let us assume
that the improbability that a dead person will
be restored to life, as deduced from past expe-
rience, is 200,000,000,000 to 1.

Let us also suppose that there are witnesses
who will speak the truth, and who are not them-
selves deceived in ninety-nine cases out of a
hundred. Now, let us examine what is the
probability of the falsehood of a statement in
which two such persons absolutely unknown
to and unconnected with each other agree.

Since the order in which independent wit-
nesses give their testimony docs not affect their
credit, we may suppose that, in a given num-
ber of statements, both witnesses tell the truth
in the ninety-nine first cases, and the false-
hood in the hundredth. Then,

The first time the second witness B testifies,
he will agree with the testimony of the first

AGAINST MIRACLES. 129

witness A, in the ninety-nine first cases, and
differ from him in the hundredth. Similarly,
in the second testimony of B, he will again
agree with A in ninety-nine cases, and differ
in the hundredth, and so on for ninety-nine
times ; so that, after A has testified a hundred,
and B ninety-nine times, we shall have

99 X 99 cases in which both agree,

99 cases in which they differ, A being wrong.

Now, in the hundredth case in which B testi-
fies, he is wrong ; and, if we combine this with
the testimony of A, we have ninety-nine cases
in which A is right and B wrong ; and one case
only in which both A and B agree in error. The
whole number of cases, which amounts to ten
thousand, may be thus divided : —

99 X 99=9801 cases in which A and B agree in truth,
1 X 99= 99 cases in which B is true and A false,

99 X 1= 99 cases in which A is true and B false,
1x1= 1 case in which both A and B agree in a

falsehood.

10,000 cases.

130 Hume's argument

As there is only one case in ten thousand
in which two such independent witnesses can
agree in error, the probabiHty of their testimony
being false is ^-^ or ^,.

The reader will already perceive how great
a reliance is due to the concurring testimony
of two independent witnesses of tolerably good
character and understanding. It appears that
the chance of one such witness being in error
is ^r, that of two concurring in the same
error is ^-^2 ; and if the same reasoning be ap-
plied to three independent witnesses, it will be
found that the probability of their agreeing in
error is ^3 ; or that the odds are 999,999 ta

1 against the agreement.

Pursuing the same reasoning, the probability
of the falsehood of a fact which six such inde-
pendent witnesses attest is ^^ or it is, in
round numbers.

AGAINST MIRACLES. 131

1,000,000,000,000 to 1 against the falsehood of their tes-
timony.

The improbability of the miracle of a dead
man being restored, is, as we have seen, on the
principles stated by Hume, 20 {m)^ 5 or it is —

200,000,000,000 to 1 against its occurrence.

It follows, then, that the improbability of the
falsehood of the concurring testimony of only
six such independent witnesses^ is already ^ve
times as great as the improbability against the
miracle of a dead man's being restored to life,
deduced from Hume's method of estimating
its probability solely from experience. As the
argument of Hume is universal, it is sufficient
for its refutation to give a single instance in
which it does not hold.

The reader will find, in a note in the Ap-
pendix, the mathematical inquiry, in which, the
degree of improbability of the miracle and

K 2

132 Hume's argument.

the degree of probability belonging to the wit-
nesses being assigned, it will be seen whether
any, and what number of such witnesses, can
outweigh the improbability of the miracle.

A PRIORI ARGUMENT. 133

CHAP. XI.

A PRIORI ARGUMENT IN FAVOUR OF THE OCCUR-
RENCE OF MIRACLES.

In the present chapter it is proposed to
prove, that —

It is more probable that any law, at the know-
ledge of which we have arrived by observation,
shall be subject to one of those violations which,
according to Hume's definition^ constitutes a mi-
racle, than that it should not be so subjected.

To show the probabihty of this, we may
be allowed again to revert to the Calculating
Engine : and to assume that it is possible to
set the machine, so that it shall calculate any

134 A PRIORI ARGUMENT.

algebraic law whatever : and also possible so to
arrange it, that at any periods, however remote,
the first law shall be interrupted for one or
more times, and be superseded by any other
law ; after which the original law shall again
be produced, and no other deviation shall ever
take place.

Now, as all laws, which appear to us regular
and uniform in their course, and to be subject
to no exception, can be calculated by the en-
gine : and as each of these laws may also be
calculated by the same machine, subject to any
assigned interruption, at distinct and definite
periods ; each simple law may be interrupted at
any point by a portion of any one of all the
other simple laws : it follows, that the class of
laws subject to interruption is far more extensive
than that of laws which are uninterrupted. It
is, in fact, infinitely more numerous. There-
fore, the probability of any law with which we
have become acquainted by observation being
part of a much more extensive law, and having,

Foil MIRACLES. 135

to use mathematical language, singular points
or discontinuous functions contained within it,
is very large.

Perhaps it may be objected, that the laws
calculated by such an engine are not laws of
nature, and that any deviation from laws pro-
duced by human mechanism does not come
within Hume's definition of miracles. To this
it may be answered, that a law of nature has
been defined by Hume to rest upon experi-
ence, or repeated observation, just as the truth
of testimony does. Now, the law produced by
the engine may be arrived at by precisely the
same means— -namely, repeated observation.

It may, however, be desirable to explain
further the nature of that evidence, on which
the fact, that the engine possesses those powers,
rests.

When the Calculating Engine has been set
to compute the successive terms of any given

136 A PRIORI ARGUMENT

law, which the observer is told will have an
apparent exception (at, for example, the ten
million and twenty-third term,) the observer is
directed to note down the commencement of
its computations ; and, by comparing these re-
sults with his own independent calculations of
the same law, he may verify the accuracy of
the engine as far as he chooses. It may then
be demonstrated to him, by the very structure
of the machine, that if its motion were con-
tinued, it would, necessarily^ at the end of a
very long time, arrive at the ten-miUionth term
of the law assigned to it ; and that, by an equal
necessity, it would have passed through all the
intermediate terms. The inquirer is now de-
sired to turn on the wheels with his own hand,
until they are precisely in the same situation
as they would have been had the engine itself
gone on continuously, to the ten-millionth
term. The machine is again put in motion,
and the observer again finds that each succes-
sive term it calculates fulfils the original law.
But, after passing twenty-two terms, he now

FOR MIRACLES. 137

observes one term which does not fulfil the
original law, but which does coincide with the
predicted exception.

The continued movement now again pro-
duces terms according with the first law, and the
observer may continue to verify them as long
as he wishes. It may then be demonstrated to
him, by the very structure of the machine, that,
if its motion were continued, it would be impos-
sible that any other deviation from the appa-
rent law could ever occur at any future time.

Such is the evidence to the observer ; and, if
the superintendent of the engine were, at his
request, to make it calculate a great variety of
different laws, each interrupted by special and
remote exceptions, he would have ample ground
to believe in the assertion of its director, that
he could so arrange the engine that any
law, however complicated, might be calculated
to any assigned extent, when there should
arise one apparent exception ; after which the

138 A PRIORI ARGUMENT

original law should continue uninterrupted
for ever.

Let us now consider the miracle alluded to by
Hume — the restoration of a dead man to life.
According to the definition of that author, our
belief in such a fact being contrary to the laws
of nature, arises from our uniform experience
against it. Our personal experience is small :
we must therefore have recourse to testimony;
and from that we learn, that the dead are never
restored to life ; and, consequently, we have
the uniform experience of all mankind since
the creation, against one assigned instance of
a dead man being so restored. Let us now
find the numerical amount of this evidence.
Assuming the origin of the human race to have
been about six thousand years ago, and taking
thirty years as the duration of a generation, we
have —

6000

— — = 200 generations.
30

FOR MIRACLES. 139

And allowing that the average population of
the earth has been a thousand millions, we
find that there have been born and have died
since the creation,

200 X 1,000,000,000
=200,000,000,000 individuals.

Such, then, according to Hume, are the odds
against the truth of the miracle : that is to say,
it is found from experience, that it is about two
hundred thousand millions to one against a
dead man having been restored to life.

Let us now compare this with a parallel case
in the calculations of the engine ; and let us
suppose the number above stated to be a hun-
dred million times as great, or that the truth of
the miracles is opposed by a number of in-
stances, expressed by twenty places of figures.

The engine may be set to count the natural
numbers — 1, 2, 3, 4, &c. ; and it shall continue

140 A PRIORI ARGUMENT

to fulfil that law, not merely for the number of
times just mentioned, for that number is quite
insignificant among the vast periods it involves ;
but the natural numbers shall follow in conti-
nual succession, until they have reached an
amount which requires for its expression above
a hundred million places of figures. If every
letter in the volume now before the reader's
eyes were changed into a figure, and if all the
figures contained in a thousand such volumes
were arranged in order, the whole together
would yet fall far short of the vast induction
the observer would have had in favour of the
truth of the law of natural numbers. The
widest range of all the cycles of astronomy and
geology combined, sink into insignificance be-
fore such a period. Yet, shall the engine, true
to the prediction of its director, after the lapse
of myriads of ages, fulfil its task, and give
that one, the Jirst and only exception to
that time-sanctioned law. What would have
been the chances against the appearance of
the excepted case, immediately prior to its

FOR MIRACLES. 141

occurrence ? It would have had, according to
Hume, the evidence of all experience against
it, with a force myriads of times more strong
than that against any miracle.

Now, let the reader, who has fully entered
into the nature of the argument, ask himself
this question : — Does he believe that such an
engine has really been contrived, and what
reasonable grounds has he for that belief?

The testimony of any single witness is small
against such odds ; besides, the witness may
deceive himself. Whether he speaks truly, will
be estimated by his moral character — whether
he deceives himself, will be estimated by his
intellectual character. The probability that
such an engine has been contrived, will, how-
ever, receive great addition, when it is re-
marked, that mathematical — and, especially,
geometrical evidence is, of all others, that in
which the fewest mistakes arise, and in which
they are most readily discovered ; and when it is

142 A PRIORI ARGUMENT.

added, that the fact of the invention of such an
engine may be deduced from the drawings
with all the force of demonstration, and that it
rests on precisely the same species of evidence
as the propositions of Euclid. Whether such an
engine could be actually made in the present
state of mechanical art, is a question of quite a
different order : it must rest upon the opinions
of those who have had extensive experience in
that art. The author has not the slightest
hesitation in stating his opinion to be, that it
is fully within those limits.

This, however, is a question foreign to the
nature of the argument, which might have been
stated in a more abstract manner, without any
reference to such an engine. As, however, it
really arose from that machine, and as visible
forms make a much deeper impression on the
mind than any abstract reasonings, it has been
stated in conjunction with that subject.

NATURE OF FUTURE PUNISHMENTS. 143

CHAPTER XII.

THOUGHTS ON THE NATURE OF FUTURE
PUNISHMENTS.

Who has not felt the painful memory of
departed folly? who has not at times found
crowding on his recollection, thoughts, feel-
ings, scenes, by all perhaps but him for-
gotten, which force themselves involuntarily
on his attention ? Who has not reproached
himself with the bitterest regret at the follies
he has thought, or said, or acted? Time
brings no alleviation to these periods of morbid
memory : the weaknesses of our youthful days,
as well as those of later life, come equally

14-4 NATURE OF

unbidden and unarranged, to mock our atten-
tion and claim their condemnation from our
severer judgment.

It is remarkable that those whom the world
least accuses, accuse themselves the most ; and
that a foolish speech^ which at the time of
its utterance was unobserved as such by all
who heard it, shall yet remain fixed in the
memory of him who pronounced it, with a
tenacity which he vainly seeks to communicate
to more agreeable subjects of reflection. It is
also remarkable that whilst our own foibles,
or our imagined exposure of them to others,
furnish the most frequent subject of almost
nightly regret, yet we rarely recall to recollec-
tion our acts of consideration for the feelings
of others, or those of kindness and benevolence.
These are not the familiar friends of our
memory, ready at all times to enter the domi-
cile of mind its unbidden but welcome guests.
When they appear, they are usually summoned
at the command of reason, from some un-

FUTURE PUNISHMENTS. 145

expected ingratitude, or when the mind retires
within its council chamber to nerve itself for
the endurance or the resistance of injustice.

If such be the pain, the penalty of thought-
less folly, who shall describe the punishment
of real guilt ? Make but the offender better,
and he is already severely punished. Memory,
that treacherous friend but faithful monitor,
recalls the existence of the past, to a mind
now imbued with finer feelings, with sterner
notions of justice than when it enacted the
deeds thus punished by their recollection.

If additional knowledge be given to us, the
consequences of many of our actions appear in
a very altered light. We become acquainted
with many evils they have produced, which, al-
though quite unintentional on our part, are yet
a subject of painful regret. But this unavailing
regret is mixed with another feeling far more
distressing. We reproach ourselves with not
having sufiiciently employed the faculties we

146 NATURE OF

possessed in acquiring that knowledge, which,
if we had attained, would have prevented us
from committing acts we now discover to have
been injurious to those we best loved.

On the other hand, the good which such
increased knowledge enables us to discover
that we have unhitentionally done, fails to pro-
duce that satisfaction always arising from a vir-
tuous motive ; and it is accompanied by the
regret that, by a sufficient cultivation of our
faculties, we might have enjoyed a still higher
satisfaction, by a more efficient service to our
fellow-creatures.

Thus, on whichsoever side we look at the
question, knowledge alone is advantageous
to virtue ; and if additional knowledge alone
were given in a future life, it would cause the
best of us to regret the errors of the present.

Let us now consider the consequences of a
higher tone of moral feeling — of a perception

FUTURE PUNISHMENTS. 147

of excellencies of character, hitherto unap-
preciated.

Without the torment arising from additional
knowledge, we may, in such circumstances,
perceive, that the pain we have inflicted for
imagined offences was quite beyond their real
deserts; and we may feel that the justice we
have done to others, has been quite dispropor-
tioned to the sacrifices they have made to
serve us.

If, without any addition to our intellectual
faculties, increased perfection were given to
our bodily senses, the same result would ensue,
Wollaston has shown, that there are sounds of
such a nature, that they can be heard by some
individuals, but are inaudible to others, — a cir-
cumstance which may arise either from the
incapacity of the parts of the ear to vibrate in
the same time as those which produced the
sound, or from the force of the sounding body
being insufficient to communicate through the

L 2

148 NATURE OF

air motion to those portions of the ear required
for the production of the sensation of hearing.

If we imagine the soul in an after stage of our
existence, connected with a bodily organ of
hearing so sensitive, as to vibrate with motions
of the air, even of infinitesimal force, and if it
be still within the precincts of its ancient abode,
all the accumulated words pronounced from
the creation of mankind, will fall at once on
that ear. Imagine, in addition, a power of
directing the attention of that organ entirely
to any one class of those vibrations : then will
the apparent confusion vanish at once ; and
the punished offender may hear still vibrating
on his ear the very words uttered, perhaps,
thousands of centuries before, which at once
caused and registered his own condemnation.

It seems, then, that with improved faculties
or increased knowledge, we could scarcely
look back with any satisfaction on our past lives
— that, to the major part of our race, oblivion

FUTURE PUNISHMENTS. 149

would be the greatest boon. If, however, in a
future state, we could turn from the contem-
plation of our own imperfections, and with in-
creiised knowledge apply our minds to the
discovery of nature's laws, and to the invention
of new methods by which our faculties might
be aided in that research, pleasure the most
unalloyed would await us at eveiy stage of
our progress.

Un clogged by the dull corporeal load of mat-
ter which tyrannizes even over our most intel-
lectual moments, and chains the ardent spirit
to its unkindred clay, we should advance in the
pursuit, stimulated instead of wearied by our
past exertions, and encountering each new dif-
ficulty in the inquiry, with the accumulated
power derived from the experience of the past,
and the irresistible efforts resulting from the
confidence of ultimate success.

Whether, then, we regard our future pros-
pects asconnected with afar higher acuteness of

150 NATURE OF FUTURE PUNISHMENTS.

our present senses — or, as purified by more
exalted moral feelings — or, as guided by in-
tellectual power, surpassing all we contem-
plate on earth, we equally arrive at the conclu-
sion, that the mere employment of such enlarged
faculties, in surveying our past existence, will
be an ample punishment for all our errors ;
whilst, on the other hand, if that Being who
assigned to us those faculties, should turn their
application from the survey of the past, to the
inquiry into the present and to the search
into the future, the most enduring happiness
will arise from the most inexhaustible source.

ON FREE WILL. 151

CHAP. XIII.

REFLECTIONS ON FREE WILL.

The great question of the incompatibility of
one of the attributes of the Creator — that of
fore-knowledge, with the existence of the free
exercise of their will in the beings he has
created, — has long baffled human comprehen-
sion ; nor is it the object of this chapter to
enter upon that difficult question.

As, however, some of the properties of the
Calculating Engine seem, although but very
remotely, to bear on a similar question, with
respect to finite beings, it may, perhaps, not
be entirely useless to state them.

152 REFLECTIONS

It has already been observed, that it is pos-
sible so to adjust the engine, that it shall change
the law it is calculating into another law at
any distant period that may be assigned.

Now, by a similar adjustment, this change
may be made to take place at a time not fore-
seen by the person employing the engine. For
example : when calculating a table of squares,
it may be made to change into a table of cubes,
the first time the square number ends in the
figures —

269696 ;

an event which only occurs at the 99736th
calculation ; and whether that fact is known to
the person who adjusts the machine or not, is
immaterial to the result.

But the very condition on which the change
depends, maybe impossible. Thus, the change
of the law from that of squares to that of
cubes may be made to take place the first time

ON FREE WILL. 153

the square number ends with a 7. But it is
known, that no square number can end in a
7 ; consequently the event, on the happening
of which the change is determined, can itself
never take place. Yet, the engine retains
impressed on it a law, which would be called
into action if the event on which it depends
could occur in the course of the law it is cal-
culating.

Nay, further, if the observer of the engine
is informed, that at certain times he can move
the last figure the engine has calculated, and
change it into any other, in consequence of
which it becomes possible that some future
term may end in 7 ; then, after he has so
changed the last figure, whenever that ter-
minal figure arrives, all future numbers calcu-
lated by the machine will follow the law of the
cubes.

154 REFLECTIONS

These contingent changes may be hmited to
single exceptions, and the arrival of such ex-
ception may be made contingent on a change
which is only possible at certain rare periods.
For example : the engine may be set to calculate
square numbers, and after a certain number of
calculations — ten million and fifty-three, for
example, it shall be possible to add unity to a
wheel in another part of the engine, which in
every other instance is immovable. This fact
being communicated to the observer, he may
either make that addition or refrain from it :
if he refrain, the law of the squares will con-
tinue for ever ; if he make the addition, one
single cube will be substituted for that square
number, which ought to occur ten million and
five terms beyond the point at which he made

ON FREE WILL. 155

the addition ; and after that no future addi-
tion will ever become possible, and no future
deviation from the law of the squares will
ever occur.

156 THE ORIGIN OF EVIL,

CHAP. XIV.

THOUGHTS ON THE ORIGIN OF EVIL.

/ had intended to have pat into writing the
substance of an interesting discussion I once
had with a distinguished Philosopher, now no
more, but other demands on my time have pre-
vented the completion of this intention.

CONCLUSION. 157

CONCLUSION.

Reader, I have now fulfilled the task I under-
took. Labouring under that imputed mental
incapacity which the science 1 cultivate has
been stated to produce^ I have brought from
the recesses of that science the reasonings and
illustrations by which I have endeavoured
faintly to embody the human conception of the
Almighty mind. It is for you to determine
whether the trains of thought I have excited
have lowered or exalted your previous notions
of the power and the knowledge of the
Creator.

1.58 CONCLUSION.

That prejudice which I have endeavoured to
expose is not a merely speculative opinion, it
is a practical evil ; and those whose writings have
been supposed to give support to it, will, I am
sure, feel grieved when they learn that it is
used by the ignorant and the designing, for the
injury of the virtuous and the instructed; that
it is employed as a firebrand, to disturb the re-
lations of social life. They will also, if the
arguments I have used have the same weight
on their minds which they have had on my
own, lament still more deeply that they should
have contributed, in any degree, to throw
discredit on that species of knowledge which
is now found to supply some of the strongest
arguments in favour of religion. I will, how-
ever, hope that the opinions I have com-
bated are not shared or even countenanced
by the higher authorities of our Protestant
Church ; and I cannot better conclude this
Fragment, than by recalling to the reader the
words of one, whose power of reasoning, and
whose love of truth, add dignity to the high
station he so deservedly fills : —

CONCLUSION. 159

*' Lastly, As we must not dare to withhold
*' or disguise revealed religious truth, so, we
" must dread the progress of no other truth.
^' We must not imitate the bigoted Romanists
** who imprisoned Galileo ; and step forward
" Bible hi hand (hke the profane Israelites car-
" rying the Ark of God into the field of battle)
*' to check the inquiries of the Geologist, the
*' Astronomer, or the Political-economist, from
'' an apprehension that the cause of religion
" can be endangered by them.^ Any theory
*' on whatever subject, that is really sound, can
*^ never be inimical to a religion founded on
^' truth ; and any that is unsound may be re-
" futed by arguments drawn from observation
" and experiment, without calhng in the aid of
" revelation. If we give way to a dread of
" danger from the inculcation of any scriptural
** doctrine, or from the progress of physical or
** moral science, we manifest a want of faith in
*/ God's power, or in his will, to maintain his

* See First Lecture on Political Economy.

160 CONCLUSION.

* own cause. That we shall indeed best fur-
^ ther his cause by fearless perseverance in an
' open and straight course, I am firmly per-
' suaded ; but it is not only when we perceive
' the mischiefs of falsehood and disguise, and
' the beneficial tendency of fairness and can-
^ dour, that we are to be followers of truth :
^ the trial of our faith is, when we cannot per-
' ceive this : and the part of a lover of truth
^ is to follow her at all seeming hazards, after
^ the example of Him who * came into the
^ world that He might bear witness to the
' Truth.'"*

* Sermons by the Archbishop of Dublin.

APPENDIX

;

APPENDIX.

NOTE A.

ON THE GREAT LAW WHICH REGULATES MATTER.

Ever since the period when Newton established the
great law of gravity, philosophers have occasionally
speculated on the existence of some more comprehen-
sive law, of which gravity itself is the consequence.
Although some have considered it vain to search for a
more general law, the great philosopher himself left
encouragement to future inquirers ; and the time, per-
haps, has even now arrived, when such a discovery may
be near its maturity. It would occupy too much space
to introduce many illustrations of this opinion ; there
is, however, one which deserves attention, because it is
not merely a happy conjecture, but the hypothesis on
which it rests has been carried by its author, through
the aid of profound mathematical reasoning, to many
of its remote consequences.

M 2

IGi' APPENDIX.

M. Mosotti* has shown, that by supposing matter
to consist of two sorts of particles, each of which repels
similar particles, directly as the mass, and inversely as
the squares, of their distances ; whilst each attracts those
of the other kind, also according to the same law, —
then the resulting attractions explain all the pheno-
mena of electricity, and there remains a residual force,
acting at ail sensible distances, according to the law of
gravity.

Many of the discoveries of the present day point
towards a more general law ; and many of the philo-
sophers of the present time anticipate its near approach.
Under these circumstances, it may be interesting as
well as useful briefly to state the principles which such
a law must comprehend ; and to indicate, however im-
perfectly, the path to be pursued in the research.

If matter be supposed to consist of two sorts of
particles, or rather, perhaps, of two sorts of centres of
force, of different orders of density ; and if the parti-
cles of each order repel their own particles, according
to a given law, but attract particles of the other kind,
according to another law, — then, if we conceive only
one particle of the denser kind to exist, and an infinite

* Professoi- of Physics at the University of the Ionian Islands. —
The paper of M. Mosotti has been translated, and published by Mr.
11. Taylor, in the third number of tlie Scientific Memoirs ; a work
which it is proposed shall contain translations of all the most important
original papers printed in foreign countries.

APPENDIX. 165

number of the other kind, that single particle will be-
come the centre of a system, surrounded by all the
others, which will form around it an atmosphere denser
near the central body.

If we conceive a stream of particles, similar to those
forming the atmosphere, to impinge upon it, so as just
to overcome its resistance, they will, whilst continually
producing undulations throughout its whole extent,
gradually increase its magnitude, until it attains such a
size, that the repulsion of the particles at its outer sur-
face is just balanced by the attraction of the central
particle. If the stream continue after this point is
reached, the whole outer layer will be pressed a little
beyond the limit of attraction, and will fly off at right
angles to the surface, which might then be said to
radiate.

If the whole of the space in which such a central
particle with its atmosphere is placed, is itself full of
atmospheric particles, then their density will increase
in approaching the central body ; and if a stream of
such particles were directed towards the centre, they
might produce throughout the atmosphere vibrations,
which would be transmitted from it in all directions.

If two such central particles, with their atmospheres,
exist at a distance from each other, they will be drawn
together by a force depending on the difference between

166 APPENDIX.

the mutual repulsion of their atmospheres and central
bodies respectively for each other, and the attraction of
each central particle for its neighbour's atmosphere : and
in order to coincide with the existing law of nature,
this must be directly as the mass, and inversely as the
square, of the distance. The other conditions which
such a law must satisfy, are —

1. That the juxtaposition of such atoms must, in
some circumstances, form a solid body.

2. In other circumstances, a fluid.

3. That again, in still other circumstances, its par-
ticles shall repel each other, or the body become
gaseous.

4. In the first state the body must possess cohesion,
tenacity, malleability, elasticity ; the measure and extent
of each of which must result generally from the origi-
nal law, and in each particular case from the constants
belonging to the substance itself.

5. In the second, it must possess capillarity, suscep-
tibihty of being compressed without becoming solid,
as also elasticity.

But besides these, the central atoms must admit of a
more intimate approach, so that their atmospheres may

APPENDIX. 167

unite and form one atmosphere. This might constitute
chemical union. Binary compounds might then (sup-
posing the distance between the two central particles to
be very small, compared with the diameters of the at-
mospheres) have atmospheres not quite spherical, and
attracting differently in ditferent directions ; thus pos-
sessing polarity. Combinations of three or more
atoms, as the central body of one atmosphere, might
give great varieties of attractive forces. Each dif-
ferent combination would give a different atmosphere ;
and the equation of its surface might, perhaps, be-
come the mathematical expression of the substance
it constituted. Thus, all the phenomena produced by
bodies, acting chemically on each other, might be de-
duced from the comparison of the characteristic surfaces
of the atmospheres of their atoms. Another result, also,
might ensue. Two or more central atoms uniting,
might either not be able to retain the same amount of
atmosphere, or they might possibly be able to retain a
larger quantity. If the particles of such atmospheres
constituted heat, it would in the former case be given
out, and in the latter absorbed by chemical union.

Hence the whole of chemistry, and with it crystal-
lography, would become a branch of mathematical
analysis, which, like astronomy, taking its constants
from observation, would enable us to predict the cha-
racter of any new compound, and possibly indicate the
source from which its formation might be anticipated.

168 APPENDIX.

For the sake of simplicity, two species of particles
only have been mentioned above ; but it seems more
probable, that matter consists of at least three kinds.

Suppose each kind to repel its own particles ; and
supposing the central atom, whilst it repels similar
particles, to attract those of the two other kinds ; and
moreover, that these latter were either repulsive, or
indifferent to each other. We might then conceive
matter to be made up of particles, each having a central
point, with an atmosphere surrounding it, and this at-
mosphere again inclosed within another and larger one.

Under such circumstances, the outer atmosphere
might give rise to heat and light, to solidity and fluidity,
and the gaseous condition ; to capillarity, to elasticity,
tenacity, and malleability. The more intimate union
of the central atoms, by which two or more become
enclosed in one common atmosphere of the second
kind, might represent chemical combinations, and per-
haps that atmosphere itself be electricity. Possibly,
also, this intermediate atmosphere, acted on by the
pressure of the external one, and by the attraction of
the central atom, might take the liquid form. These
binary or multiple-combinations of the original atoms,
and their smaller atmospheres, would still be enclosed
in an atmosphere of the outer kind, which might be
nearly spherical. The joint action of the three might,
at sensible distances, produce gravity.

APPENDIX. 169

The reader should, however, bear in mind, that
these hints are but thrown out as objects of reflection
and inquiry ; and that nothing but a profound mathe-
matical investigation can establish them, or even give
to them that temporary value which arises from any
hypothesis, representing a large collection of facts.

170 APPENDIX.

NOTE B.

ON THE CALCULATING ENGINE.

The nature of the arguments advanced in this volume
having obhged me to refer, more frequently than I
should have chosen, to the Calculating Engine, it be-
comes necessary to give the reader some brief account
of its progress and present state.

About the year 18S1, I undertook to superintend,
for the Government, the construction of an engine for
calculating and printing mathematical and astronomical
tables. Early in the year 1833, a small portion of the
machine was put together, and it performed its work
with all the precision which had been anticipated. At
that period circumstances, which I could not control,
caused what I then considered a temporary suspen-
sion of its progress ; and the Government, on whose

APPENDIX. 171

decision the continuance or discontinuance of the work
depended, have not yet communicated to me their
wishes on the question. The first illustration I have
employed is derived from the calculations made by
this engine.

About October, 1834, I commenced the design of
another, and far more powerful engine. Many of the
contrivances necessary for its performance have since
been discussed and drawn according to various prin-
ciples ; and all of them have been invented in more
than one form. I consider them, even in their pre-
sent state, as susceptible of practical execution ; but
time, thought, and expense, will probably improve
them. As the remaining illustrations are all drawn
from the powers of this new engine, it may be right to
state, that it will calculate the numerical value of any
algebraical function — that, at any period previously
fixed upon, or contingent on certain events, it will cease
to tabulate that algebraic function, and commence the
calculation of a different one, and that these changes
may be repeated to any extent.

The former engine could employ about 120 figures
in its calculations; the present is intended to compute
with about 4,000.

Here I should willingly have left the subject ; but
the public having erroneously imagined, that the sums

ITS APPENDIX.

of money paid to the workmen for the construction of
the engine, were the remuneration of ray own services,
for inventing and directing its progress ; and a Com-
mittee of the House of Commons having incidentally
led the public to believe that a sum of money was voted
to me for that purpose, I think it right to give to that
report the most direct and unequivocal contradiction.

APPENDIX. 17.3

NOTE C.

EXTRACT FROM THE THEORY OF PROBABILITIES OF

LAPLACE.

" Nous devons done envisager I'etat present de Tuni-
vers, comme I'efFet de son etat anterieur, et comme la
cause de celui qui va suivre.

*' Une intelligence qui pour un instant donnee, con-
naitrait toutes les forces dont la nature est animee, et
la situation respective des etres qui la composent, si
d'ailleurs elle etait assez vaste pour soumettre ces don-
nees a I'analyse, embrasserait, dans la meme formule,
les mouvemens des plus grands corps de I'univers et ceux
du plus 16ger atome : rien ne serait incertain pour elle,
et I'avenir, comme le passe, serait presept a ses yeux.
L'esprit humain offre, dans la perfection qu'il a su don-
ner a I'astronomie, une faible esquisse de cette intelli-

174 APPENDIX.

gence, Ses decouvertes en mecanique et en georaetrie,
jointes a celle de la pesanteur universelle, I'ont mis a
portee de comprendre dans les memes expressions ana-
lytiques, les etats passes et futurs du systeme du
monde.

*' En appliquantle meme methode a quelques autres
objets de ses connaissances, il est parvenu k ramener
h des lois generates, les phenomenes observes, et a
prevoir ceux que des circonstances donnees doivent
faire eclore. Tous ses efforts dans la recherche de la
verite, tendent a le rapprocher sans cesse I'intelligence
que nous venons de concevoir, mais dont il restera
toujours infiniment eloign^. Cette tendance propre k
I'espece humaine, est ce qui la rend superieure aux
animaux ; et ses progres en ce genre, distinguent les
nations et les siecles, etfondent leur veritable gloire." —
Laplace, TMorie Analytique des Probabilites,

APPENDIX 175

NOTE D.

NOTE TO CHAP. VIII. ON MIRACLES.

The view taken of miracles in Chapter VIII. is the
same as that contained in the work of Butler, on the
Analogy of Religion to the Constitution and Course
of Nature. Inquiries connected with the Calculating
Engine, impressed it very forcibly on my own mind,
and I have drawn the illustrations chiefly from that
subject. I cannot, however, forbear referring the
reader to the opinion of Sir J. Herschel, expressed at
the beginning of his letter to Mr. Lyell, (see Note I.)
because it confirms me in the belief, that the more pro-
foundly we inquire into the mechanism of nature, the
more certainly we arrive at that conclusion.

176 APPENDIX.

NOTE E.

NOTE TO CHAPTER X. ON HUMe's ARGUMENT
AGAINST MIRACLES.

The example in the text is sufficient to show that
the conclusion at which Hume arrived respecting the
sufficiency of testimony to support a miracle, will not
bear the test of a numerical examination. It may,
however, be interesting to point out the amount of tes-
timony required, under different circumstances.

The reader will observe, that throughout the chapter
to which this note refers, as well as in the note itself,
the argument of Hume is taken strictly according to
his own interpretation of the terms he uses, and the
calculations are founded on them ; so that it is from
the very argument itself, when fairly pursued to its
full extent, that the refutation results.

APPENDIX. 177

Both our belief in the truth of human testimony,
and our beUefin the permanence of the laws of nature,
are, according to Hume, founded on experience; we
may, therefore, in the complete ignorance in which he
assumes we are, with respect to the causes of either,
treat the question as one of the probability of an event
deduced solely from observations of the past.

If an event has been observed to happen m times in
succession, it is known that the probability of its hap-

pening the next time is ^ , and the probability of

its not arriving is — —- ^ .* If we suppose m to repre-
sent the amount of the uniform experience of all
mankind, from the creation to the present time, it will

be a very large number, and ^ will represent the

probability of the occurrence of a miracle opposed to
that experience.

Again : if it is found from experience, that a certain
class of men out of every p statements, make one of
them false, either from ignorance or design, then the

* " On trouve ainsi qu'un ev^nement etant arrive de suite, un
nombre quelconque de fois ; la probabilite qu'il arrivera encore la
fois suivante est egale a ce nombre augment^ de I'unite, divise par
le meme nombre augment^ de deux unites." — Laplace's Theorie Ana-
lytiqne des Probabilites, p. xiii.

178 APPENDIX.

probability of the falsehood of a statement made by
such a person, is 1

The probability that two such persons will concur
in falsehood, is ]

^'
and the probability of the concurrence of n such per-
sons in an error, is 1

Now, according to Hume's argument, the falsehood
of the testimony by which a miracle is supported, must
be a more miraculous event than the occurrence of the
miracle itself.

Here, then, we have for the measure of the improba-
bility of the testimony —^^ , and for that of the occur-
rence of the miracle ; and, in order to prove

m-\-2 ^

the miracle, the first improbability must be greater
than the second. But this can only happen when

p^^ m + 2.
Hence, n log. p ^ log. (?/2 + 2)

and „>J5g_(^±l).
^ iog.p

It follows, therefore, that however large m may be,
or however great the quantity of experience against the

APPENDIX. 179

occurrence of a miracle, (provided only that there are
persons whose statements are more frequently cor-
rect than incorrect, and who give their testimony in
favour of it without collusion,) a certain number n can
ALM^AYs be found ;^ so that it shall be a greater irrir
probability that they shall agree in error^ than that the
miracle shall occur.

Let us suppose each of the witnesses who gives
independent testimony, makes one erroneous state-
ment in ten; then

" > log. 10 > ^°S- (»» + 2).

And, moreover, let us suppose the number of places
of figures contained in tw + 2, to be ^ ; then log. {m + 2)
is nearly equal to ^^ — 1 , and

n^h— 1.

Now let the number of observed instances in which
the miracle has not occurred be a million million;

or, 1,000,000,000,000,

then the number of such witnesses necessary to prove
its occurrence is

w>log.(10^H2)>12,

or thirteen such witnesses are sufficient.

If J) = 100, then we must have for the number
of such witnesses,

N 2

180 APPENDIX.

^ log, {m + 2)^ log, (m + 2)
-^ log. 100 -^ 2 '

and if, as before, 7n is a million millions,

or seven witnesses, are sufficient.

It may be proper to remark, that if a person has
established his power to work a miracle in one or more
instances, the probability of his being able to do so in
any other case becomes considerable, whatever may be
the probability of his usual statements. For, as we have
observed that in the one or more instances in which
he stated that he should perform a miracle, the event
followed his prediction ; and, also, that in no instance
it failed to follow such prediction : we must treat the
case in the same manner as the occurrence of an event
m times in succession ; and, if he have performed m
miracles, the probability that he will perform any other
which he predicts is m -\-l

m + 2'
or, if he has performed a miracle only once, it is two
to one that he has power to perform the next miracle
he predicts.

The view explained in the chapter of the text to
which this note refers, was takei^ previously to my pe-
rusal of the observations of Dr. Chalmers " on the

APPENDIX. 181

power which lies in the concurrence of distinct testi-
monies,"* contained in a work pointed out to me by
a friend to whom I had mentioned the subject. Dr.
Chalmers' view is, I believe, substantially the same as
my own, as far as relates to the effect of concurrent
testimony ; and had the nature of his work admitted
the introduction of algebraic operations, he would,
most probably, have combined it with the other
principle I have employed, of the probability of the
occurrence of a future event from observations of the
past, and thus have arrived at the complete answer to
the argument of Hume against miracles, by not only
showing the possibility of supporting them by testi-
mony, but even of ascertaining, in any given circum-
stances, the precise number of witnesses required.

* Evidences of the Christian Revelation, vol i. p. 129.

182

APPENDIX.

NOTE F.

ON THE CONSEQUENCES OF CENTRAL HEAT.

The increase of temperature observed as we descend
below the earth's surface, as well as other pheno-
mena, have led to a very general opinion, that great
heat exists in the interior of the earth, and that the
body of our planet, having been at one time intensely
heated, has cooled down to its present temperature.
With the view of pointing out courses of inquiry, by
which these opinions may ultimately be tested by ob-
servation, it is expedient to take a cursory view of
some of the consequences of such an hypothesis.

And first, let us imagine the exterior of our globe to
have once been in a state of intense heat. No fluid
such as water could then have existed on its surface :
it would instantly have been converted into vapour ; and

APPENDIX. 183

notwithstanding the increased weight of atmosphere
thus produced, and pressing on its surface, sufficient
heat would have reduced all fluids to the gaseous state.
Let us, however, inquire as to the possible extent of
such an atmosphere.

In the first place, it could not extend beyond that
point at which the moon's attraction is equal to that
of the earth. In the next place, much more con-
tracted limits would be prescribed by the effect of
centrifugal force, and of the cooling of the vapour by
expansion, and by its distance from the source of ra-
diant heat, which had produced that state.

It would be interesting to inquire, what would be
the nature of the surface of the atmosphere under such
circumstances. At the distance at which the centrifugal
force is equal to that of gravity, it might happen that
the temperature was scarcely sufficient to maintain the
water in a gaseous state. Should this have been the
case, a belt of perpetual clouds might have been formed,
resembling those of Jupiter.

If, at this limit, a still lower degree of temperature
prevailed, instead of a belt of clouds, a ring of ice
might be formed.

This ring of ice, being exposed to different eflTects of
radiation from various parts of the earth's surface.

184 APPENDIX.

might, by the superior heat at one part, become di-
minished, whilst the condensation of vapours might
augment less exposed parts : and these conditions
might continue, until at last the ring itself was melted
through at one point, and the whole would fall down
on the surface of the planet. The tearing up of that
surface from such an event, would be augmented by
the sudden conversion of the solid ice into steam ; and
after a time, the fragments of the ring would be ab-
sorbed again into the atmosphere of the planet.

Let us now suppose, owing to the gradual cooling
down of the whole globe, the limit of condensation of
steam into water, to occur at a nearer point than that at
which the centrifugal force equals that of gravity. As
soon as the steam is condensed into water, it will de-
scend towards the surface of the earth ; but that surface
being still very hot, will, by its radiation, again con-
vert the descending shower into steam ; and this will
happen at different heights above the surface, accord-
ing to the radiating power of the part below. We
may, therefore, conceive a shell surrounding the earth,
the outer surface of which has just been condensed into
water, and the inner consists of vapour, just re-con-
verted into that state by the earth's radiation. These
surfaces will attain different heights in different places.
Between these two surfaces there will exist a perpetual
rain, descending from the upper as a gentle shower,
becoming gradually a violent current, and then as

APPENDIX. 185

it falls re-absorbed into another gentle shower, which
is entirely absorbed in approaching the heated surface.
Such being the state of things, let us imiigine the
globe to cool down uniformly. The lower surface of
the descending rain, which is placed at irregular
heights, will at length be brought down to the earth's
surface in one or more points. The effect of this, which
will in the first instance be a gentle shower, would be
to cool that portion of the surface on which it falls, and
hence to diminish its radiating power. This change, in
its turn, will lower the under surface of the watery shell,
so that a more violent rain, and ultimately an impetuous
torrent will continue, perhaps, for thousands of years,
its unintermitted vertical action on the surface exposed
to its force. The excavation of the largest valleys, or
even of ocean beds, is not too much to expect from
such forces.

But let us take another view of the consequences of
such an original state of incandescence. The whole of
the fluids now on the surface of the earth must then
have been suspended in its atmosphere. But the ex-
tent of that atmosphere is itself limited by various
causes : the attraction of other bodies, the eifects of
centrifugal force, the decrease of temperature, and the
distances at which the particles of gaseous bodies cease
to repel each other, all have their influence in deter-
mining its form and magnitude. Let us suppose that
we possessed data from which the approximate amount

186 APPENDIX.

of vapour contained in the entire atmosphere were
known, and consequently the whole amount of water
in it ; then, since we know the area of the present seas,
we might easily ascertain their average depth. If the
result of such a computation should give a mean depth
much less than that which we know the ocean to pos-
sess,— as, for instance, only a hundred feet, — then we
might conclude, either that the surface of the earth had
never been in such a state of incandescence as has been
supposed, or that if it had, that a new source of aqueous
vapour had been supplied to it, subsequently to its
cooling down.

APPENDIX 225

acts upon, would produce ripple of larger size than
would otherwise occur.

The surface of the sun presents to very good tele-
scopes a certain mottled appearance, which is not
exactly ripple, and which it is difficult to convey by
description. It may, however, be suggested, that
wherever such appearances occur, whether in planetary
or in stellar bodies, or in the minuter precincts of the
dye-house and the engine-boiler, they indicate the
fitness of an inquiry, whether there are not two cur-
rents of fluid or semi-fluid matter, one moving with a
different velocity over the other, the direction of the
motion being at right angles to the lines of waves.

226 APPENDIX.

NOTE M.

ON THE AGE OF STRATA, AS INFERRED FROM THE
RINGS OF TREES EMBEDDED OF THEM.

The indelible records of past events which are pre-
served within the solid substance of our globe, may be
in some measure understood without that refined ana-
lysis on which their complete knowledge depends.
The remains of vegetation, and of animal life, em-
bedded in their coeval rocks, attest the existence of other
times ; and as science and the arts advance, we shall
be enabled to read the minuter details of their living
history. The object of the present note is to suggest
to the reader a line of inquiry, by which we may still
trace some small portion of the history of the past in
the fossil woods which occur in so many of our strata.

It is well known that dicotyledonous trees increase
in size by the deposition of an additional layer annually

APPENDIX. 227

between tlie wood and the bark, and that a transverse
section of such trees presents the appearance of a series
of nearly concentric irregular rings, the number of
which indicates the age of the tree. The relative
thickness of these rings depends on the more or less
flourishing state of the plant during the years in which
they were formed. Each ring may, in some trees, be
observed to be subdivided into others, thus indicating
successive periods of the same year during which its
vegetation was advanced or checked. These rings are
disturbed in certain parts by irregularities resulting
from branches ; and the year in which each branch first
sprung from the parent stock may be ascertained by
proper sections.

It has been found by experiment, that even the
motion imparted to a tree by the winds has an influ-
ence on its growth. Two young trees of equal size
and vigour w^ere selected and planted in similar circum-
stances, except that one was restrained from having
any motion in the direction of the meridian, by two
strong ropes fixed to it, and connecting it to the ground,
at some distance to the north and south. The other
tree was by similar means prevented from having any
motion in the direction of east and west. After several
years, both trees were cut down, and the sections of
their stems were found to be oval ; but the longer axis
of the oval of each was in the direction in which it had
been capable of being moved by the winds.

^22S API'ENDIX.

These prominent effects are obvious to our senses;
but every shower that falls, every change of tempe-
rature that occurs, and every wind that blows, leaves on
the vegetable world the traces of its passage ; slight,
indeed, and imperceptible, perhaps, to us, but not the
less permanently recorded in the depths of those
woody fabrics.

All these indications of the growth of the living
tree are preserved in the fossil trunk, and with them
also frequently the history of its partial decay. Let
us now examine the use we may make of these details
relative to individual trees, when considering forests
submerged by seas, embedded in peat mosses, or
transformed, as in some of the harder strata, into stone.
Let us imagine, that we possessed sections of the
trunks of a considerable number of trees, such as those
occurring in the bed called the Dirt-bed,* in the island
of Portland. If we were to select a number of trees
of about the same size, we should probably find many
of them to have been contemporaries. This fact would
be rendered probable if we observed, as we doubtless
should do, on examining the annual rings, that some
of them conspicuous for their size occurred at the same
distances of years in several trees. If, for example, we

* The reader will find an account of these fossil trees, and the strata
in which they occur, in several papers by Dr. Buckland, Mr, De la
Beche, and Dr. Fitton, in the Transactions of the Geological Society
of London, vol. iv. Series 2.

APPICNDIX. 229

found on several trees a remarkably large annual ring,
followed at the distance of seven years by a remarkably
thin ring, and this again, alter two years , followed by
another large ring, we should reasonably infer from these
trees, that seven years after a season highly favourable to
their growth, there had occurred a season peculiarly
unfavourable to them: and that after two more years
another very favourable season had happened, and that
all the trees so observed had existed at the same period
of time. The nature of the season, whether hut or
cold, wet or dry, would be known with some degree of
probability, from the class of tree under consideration.
This kind of evidence, though slight at first, receives
additional and great confirmation by the discovery of
every new ring which supports it; and, by a consider-
able concurrence of such observations, the succession
of seasons might be in some measure ascertained at
remote geological periods.

On examining the shape of the sections of such
trees, we might perceive some general tendency to-
wards a uniform inequality in their diameters ; and we
might perhaps observe that the longer axes of the
sections most frequently pointed in one direction. If
we knew from the species of tree that it possessed no
natural tendency to such an inequality, then we might
infer that, during the growth of these trees, they were
bent most frequently in one direction ; and hence an
indication of the prevailing winds at that time. In

230 APPENDIX.

order to find from which of the two opposite quarters
these winds came, we might observe the centres of
these sections ; and we should generally find that the
rings on one side were closer and more compressed
than those on the opposite side. From this we might
infer the most exposed side, or that from which the
wind most frequently blew. Doubtless there would
be many exceptions arising from local circumstances —
some trees might have been sheltered from the direct
course of the wind, and have only been acted upon by an
eddy. Some might have been protected by an adjacent
large tree, sufficiently near to shelter it from the ruder
gales, but not close enough to obstruct the light and
air by which it was nourished. Such a tree might have
a series of large and rather uniform rings, during the
period of its protection by its neighbour; and these
might be followed by a series of stinted and irregular
ones, occasioned by the destruction of its protector.
The same storm might have mutilated some trees, and
half-uprooted others : these latter might strive to sup-
port themselves for years, making but little addition, by
stinted layers, to the thickness of their stems; and then,
having thrown out new roots, they might regain their
former rate of growth, until a new tempest again
shook them from their places. Similar eflfects might
result from floods and the action of rivers on the
trees adjacent to their banks. But all these local
and peculiar circumstances would disappear, if a
sufficient number of sections could be procured from

APPENDIX. 231

fossil trees, spread over a considerable extent of
country.

Similar rings might however furnish other inti-
mations of a successive existence of these trnes.

On examining some rings remarkable for their size
and position, we might find, for instance, in one sec-
tion, two remarkably large rings, separated from
another large ring, by one very stinted ring, and this
followed, after three ordinary years, by two very small
and two very large rings. Such a group might be
indicated by the letters —

oLLsooosLLoo
where o denotes an ordinary year, or ring, L a large
one, and s a small or stinted ring.

If such a group occurred in the sections of several
different trees, it might fairly be attributed to general
causes.

Let us now suppose such a group to be found near
the centre of one tree, and towards the external edge
or bark of another; we should certainly conclude,
that the tree near whose bark it occurred was the more
ancient tree ; that it had been advanced in age when
that group of seasons occurred which had left their
mark near the pith of the more recent tree, which
was young at the time those seasons happened. If,

2S2 APPENDIX.

on counting the rings of this tree, we found that there
were, counting inward from the bark to this remark-
able group, three hundred and fifty rings, we should
justly conclude that, three hundred and fifty years
before the death of this tree, which we will call A,
the other, which we will call B, and whose section we
possess, had then been an old tree. If we now search
towards the centre of the second tree B, for another
remarkable group of rings ; and if we also find a similar
group near the bark of a third tree, which we will call
C ; and if, on counting the distance of the second
group from the first in B, we find an interval of 420
rings, then we draw the inference that the tree A, 350
years before its destruction, was influenced in its
growth by a succession of ten remarkable seasons,
which also had their effect on a neighbouring tree B,
which was at that time of a considerable age. We
conclude further, that the tree E was influenced in its
youth, or 420 years before the group of the ten seasons,
by another remarkable succession of seasons, which also
acted on a third tree, C, then old. Thus we connect
the time of the death of the tree A with the series of
seasons which affected the tree C in its old age, at a
period 770 years antecedent. If we could discover
other trees having other cycles of seasons, capable of
identification, we might trace back the history of that
ancient forest, and possibly find in it some indications
for conjecturing the time occupied in forming the stratum
in which it is embedded.

APPENDIX. 2SS

The application of these views to ascertaining the
age of submerged forests, or to that of peat mosses,
may possibly connect them ultimately with the chrono-
logy of man. Already we have an instance of a wooden
hut with a stone hearth before it, and burnt wood on
it, and a gate leading to a pile of wood, discovered at
a depth of fifteen feet below the surface of a bog in
Ireland : and it was found that this hut had probably
been built when the bog had only reached half its
present thickness, since there were still fifteen feet of
turf below it.

The realization of the views here thrown out will
require the united exertions of many individuals pa-
tiently exerted through a series of years. The first
step must be to study fully the relations of the annual
rings in every part of an individual tree. The efiect
of a favourable or unfavourable season on a section
near the root must be compared with the influence of
the same circumstance on its growth towards the top of
the tree. Vertical sections also must be examined in
order to register the annual additions to its height, and
to compare them with its increase of thickness. Every
branch must be traced to its origin, and its sections
be registered. The means of identifying the influence
of different seasons in various sections of the same indi-
vidual tree and its branches being thus attained, the
conclusions thus arrived at must be applied to several
trees under similar circumstances, and such modifica-

234^

APPENDIX.

tions must be applied to them as the case may require ;
and before any general conclusions can be reached re-
specting a tract of country once occupied by a forest,
it will be necessary to have a considerable number of
sections of trees scattered over various parts of it.

APPENDIX. 235

NOTE N.

ON A METHOD OF MULTIPLYING ILLUSTRATIONS
FROM WOOD-CUTS.

Finding the number of wood-cuts necessary to
explain the parts of the Calculating Engine consider-
able, and the expense great, it appeared to me that
the method of copying by casting might, perhaps, be
employed for the purpose of diminishing the evil.

The plan which occurred to me was, to make a
drawing of that portion of the mechanism required to
be explained, which should contain every part neces-
sary for its action, and, in some cases, even the frame-
work requisite for its support. Such a drawing would
be far too complicated for the ordinary reader, and
might appear confusion even to the contriver of the
machine. This drawing was then to be sent to the
wood-cutter to be engraved, and on its return, it was to
be sent to the stereotype founder, for the purpose of

236 APPENDIX.

having any number of fac-similes made in type-metal.
Now, each of these plates would, like the original
wood-cut, express the drawing in reliefs and, by cut-
ting away any line in the plate, that line would be re-
moved in the impression.

The first thing to be done was, to remove from one
of these stereotype plates every line, except those which
formed \he framing of the mechanism. The next step
was, to remove from another of those plates all the
framing, and every other line, except those which re-
presented two or three of the principal wheels and
levers.

If there should be many such parts, several plates
might be taken, on each of which some few parts, not
interfering with each other, might be allowed to re-
main. Other plates might then be taken, on which
the parts given on two or more of the former plates,
might be allowed to remain, and other plates might
again contain combinations of three or more of these.
Thus, by a series of plates, commencing with the sim-
plest portions of the mechanism, we might gradually
advance through the various combinations, up to the
original wood-cut, which, by means of such steps,
might be made perfectly intelligible.

The original wood-cut will be more expensive, on
account of the additional work contained in it ; but its

APPENDIX. U

multiplication by casting is a cheap process; and the
cutting away some of the hnes of each plate, and
dotting others, by removing small portions at short
intervals, which might, in different plates, require to be
represented as passing behind other lines, is not a
work of much difficulty or expense. The quantity of
illustrations, all printed with the letter-press, which
this plan admits of, renders it possible to explain much
more complicated machinery than could be accom-
plished by engraving, unless at an expense which
would effectually preclude its application ; whilst the
successive picture of every wheel and lever, exhibited
on separate plates if necessary, as well as of every
one of those binary and other combinations which are
employed, will render the machinery intelligible to
a much larger class of persons than those who usually
study such subjects.

The same principle may be applied to coloured
geological sections and maps. The whole drawing
having been sent to the wood-cutter, as many stereo-
type fac-similes may be made from his block as there
are colours to be represented. One plate may then be
taken, from which all the parts are to be scraped out
which are not to be coloured brown ; another may be
taken from which all parts not to be coloured green ;
and so on for all the rest of the colours. The perfect
identity of the plates will render it easy to preserve
what is technically termed the register, that is, to

238 APPENDIX.

prevent the overlapping of any one colour on any
other.

As the method here suggested is extremely simple
in its means, it is scarcely possible but that it must
have occurred to others ; and it may, perhaps — al-
though I am not aware of it — have been employed on
some occasions. I have, however, thought, that in
giving publicity to it, I should be doing a service to
those whose writings require pictorial illustration, and
especially to those who cultivate the sciences of me-
chanics and geology. Perhaps, also, the same system
might be applied to multiply, at a cheap rate, the
blocks used in colour printing, both upon paper and
on woven fabrics.

On the opposite page, the reader will find an illus-
tration of this art ; it is the same plate as that at page
190: it is not very favourable either as to the degree
of difficulty, or as to the question of economy ; but it
is the only one that the subject of this volume ad-
mitted, and is quite sufficient to explain the principle.

The figure at the bottom of the page. No. 4, is the
impression from a stereotype plate, which is a fac-
simile from the original wood-cut, engraved for the
illustration. No. 3, the next above, is the impression
from another stereotype plate, from which the lines
marked D and F, on No. 4, have been cut away.

G —

No. 1.

•-. F

A -

No. 2.

.,.p

No. 3.

— B

— C

No. 4,

-.E
- F

240 APPENDIX.

No. 2 is the impression from another plate from which
the line E has been cut away ; and No. 1 is an im-
pression from a similar plate, from which the lines C
and E have been cut out.

The four individual plates have been soldered toge-
ther, and form the stereotype plate of the page re-
ferred to.

THE END.

R. CLAY, PRINTER, BREAD-STREET-HILL.

A-

CORRECTIONS, 241

Corrections to Chapter X, and Note E, of the First
Edition of the Ninth Bridgewater Treatise.

Some confusion and error has arisen in the statement of the reason-
ing by which the refutation of Hume's argument against m.iracles is
supported, although the conclusion itself is perfectly correct. Those
who are best acquainted with the extreme difficulty and delicacy of the
application of mathematics to the doctrine of chance, will most readily
excuse the author for his inattention. It may, however, be useful to
point out two of the sources of mistake.

The first results from the different interpretations which may be put
on Hume's statement, the second arises from the meaning of the words
probability and improbability.

In common language, an event is said to be probable when it is
more likely to happen than to fail : it is said to be improbable when it
is more likely to fail than to happen.

Now, an event whose probability is, in mathematical language, —

P
will be called probable or improbable, in ordinary language, according

as p is less or greater than 2.

If, in mathematical language, — expresses the probability of an
event happening, 1 expresses the probability of its failing, or the

improbability of its happening.

Another source of error has arisen from not distinguishing between
the probability of independent witnesses concurring in a statement
before they make it, and the probability of the truth of their testimony
after they have given it.

Throughout the inquiry, the term falsehood is applied generally to
error, whether arising from accident or intention.

THE READER IS REQUESTED TO MAKE THE ALTERATIONS
IN THE TEXT WITH A PEN.

Page 120, last line but 3, read — " that the fact did not
occur."
„ — last line, read-^^^ that the fact did not occur."

242 CORRECTIONS.

Page 121, lines 5 and [6, read, " would be more
probable than that the fact which it
endeavours to establish did not occur."

„ — line 11, ybr "probability" r^ac? " improba-
bility."

„ 125, line 7, for " true" read " false."

„ 127, and to the end of the Chapter. — It is to
be observed that the whole of this reasoning applies
only to the inquiry into the chance of the concurrence
of independent witnesses previously to their giving
their testimony.

The probability, after they have concv/rred, which
that concurrence gives to the truth of the event,
must be deduced from the following inquiry, which
should be substituted for that in the note E, p. 176.

Let us now examine the probability of the truth of
an event (whose probability, unsupported by any testi-
mony, is -) attested to have occurred by the testimony
of n independent, uncoUusive witnesses, whose proba-
bility of falsehood is — for each.

There are two views which may be taken of the
improbability of miracles. We may suppose an urn to
contain balls of only two colours, white and black,
from which m balls have been drawn, all black ; and
the event testified is, that a white ball was the

m + V-^.

Or we may consider the urn to contain m numbers,
and the testimony to assert that a given number i was
drawn at the first extraction.

The former of these cases is that which is analogous

CORRECTIONS. 243

to the miracle alluded to in the text. It has been
observed that m persons have died without any re-
surrection, and the probability of the death without

Tit ~\~ 1

resurrection of the (m + 1)*^^ is -p: , and the im-

probability of such an occurrence, independently of

testimony, is ^ ; which is therefore the probability

of a contrary occurrence, or that of a person being
raised from the dead.

Now only two hypotheses can be formed, collusion
being, by hypothesis, out of the question : either the
event did happen, and the witnesses agree in speaking
the truth, the probability of their concurrence being

/ 1\" 1
i\ f , and of that of the hypothesis being ^ ;

or the event did not happen, and the witnesses agree
in a falsehood, the probability of their concurrence

(J \ ** . 771 "4" 1
- ^ , and that of the hypothesis — .

The probability of the witnesses speaking truth,
and the event occurring, is therefore,
K'^ 1

(l - -")

V p/ m + 2 {p—iy

/ J __ 1 \" 1 / W' m+i "" {p-\Y + w + 1 '

V p/ m + % \ p ^ m-\-2

and the probability of their falsehood is,

J' m + 1

p / m + 2 m -\- \

V pJ m + 2 Vjt?/ m-\-2

But, according to Hume's argument, the falsehood
of the witnesses must be more improbable than the

244 CORRECTIONS.

occurrence of the miracle. But the probability of

the occurrence of the miracle, independent of testi-

1
mony, is — — ^ .

Tj m + I ^ \
rlence, , ^t— <r 7: :

dr (w^ + 1) . (m + 2) < {p — \Y -V rn. ^- \ \

{p-\Y >(m+l).(m + 2)-(m + l) >(m+l)2;

which is true, if

^^ ^ ^,log. (m + 1)
log. (/? - 1)

It follows, therefore, that however large m may be,
or however great the quantity of experience against
the occurrence of a miracle, (provided only that there
are persons whose statements are more frequently cor-
rect than incorrect, and who give their testimony in
favour of it without collusion,) a certain number n can
ALWAYS be found; so that it shall he a greater im-
probability that their unanimous statement shall be a
falsehood, than that the miracle shall occur.

Let us now suppose each witness to state one
falsehood for every ten truths, or jt> = 11, and
m = 1000,000,000,000;

then..>^'"f-('";!+^)>24.
^ log. 10 ^

or twenty-five such witnesses are sufficient.

If the witnesses only state one falsehood for every
hundred truths, then thirteen such witnesses are
sufficient.

..'Y-

sfl«v>w;!^*!f-';^^.--

'f^\

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Full text of "The ninth Bridgewater treatise; a fragment"

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